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Math Help - Word problem: Cost function, Revenue Function, Profit function.

  1. #16
    MHF Contributor

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    Re: Word problem: Cost function, Revenue Function, Profit function.

    What you originally posted said, "each bottle costs .5 cents", which would be neither $0.5 nor $0.05 but $0.005.
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  2. #17
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    Re: Word problem: Cost function, Revenue Function, Profit function.

    Quote Originally Posted by HallsofIvy View Post
    What you originally posted said, "each bottle costs .5 cents", which would be neither $0.5 nor $0.05 but $0.005.
    we cleared up that misinterpretation in posts 11-13

    5 cents and 65 cents
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  3. #18
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    Re: Word problem: Cost function, Revenue Function, Profit function.

    Thanks a lot guys for all your help.
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  4. #19
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    Re: Word problem: Cost function, Revenue Function, Profit function.

    1-A retail company plans to work on a margin of 44% of retail price and to incur other variable costs of 4%. If it expects fixed costs of $20,000,
    a)Find the equation relating total cost to sales
    b)Find the profit it sales are $60,000.
    c) Find breakeven revenue.
    d) If profit is $15,000, what should be the revenue levels?
    e) If the company has only one item at a price of$15 per unit, how do you convert the cost equation in terms of revenue in a cost equation in terms of quantity?
    2-A small home business is set up with an investment of $1,000,000 for equipment. The business manufactures a product at a cost of a $60 per unit. if the product sells for $140, how many units must be sold before the business break even?
    3-A certain car model cost $20,000 with a gasoline engine and $25,000 with a diesel engine. The number of miles per gallon of fuel for cars with these two engines is 25 and 30, respectively.Assume that the price of both types of fuel is $1.50 per gallon.
    a) Drive the equation for the cost driving a gasoline powered car.
    b) Drive the equation for the cost of driving a diesel powered car.
    c)Find the breakeven point, that is ,find the mileage at which the diesel-powered car becomes more economical than the gasoline powered car.
    4-During its first year of operation,Adidas company had total sales of 25,000 units with selling price of $100, total variable costs of $1,500,000 and total fixed cost of $350,000
    a)Develop revenues,cost,and profit functions for the company in terms of quantity.
    b) Find the break-even point in terms of quantity.
    c) Convert the cost equation in terms of quantity in to a cost equation in terms of revenue.
    d) Find the break- even revenue.
    e) If profit had been $500,000 what would have been the sales volume (revenue) and the quantity of sales.
    f) what would have been the profit if sales were $2,000,000?
    5- A firm manufactures and markets a product that sells for $20 per unit. Fixed costs associated with activity total $40,000 a month, while variable cost per unit is $10.A maximum of 10,000 units can be produced and sold.
    a) Drive the total revenue, total cost and total profit functions.
    b) Sketch the total revenue, total cost and total profit functions in the same coordinate system.
    c) What is the break-even point (in terms of quantity and sales volume)?
    d) Drive the new total cost, total profit functions given that fixed cost is increased by $10,000 a month, and calculates the new break-even point.
    e) Drive the new total cost and total profit functions given that unit variable cost is decreased by 20% and calculate the new break-even point.
    f) Drive the new total revenue and total profit functions given that the unit selling price increases by 20% and calculates the new break-even point.
    g) What is the relationship that you may inter from break-even point and fixed cost,selling price and break-even point and unit variable cost and break-even point?
    h) Assume selling price increases by 10% and at the same time unit variable cost increases by 10%what is the effect of these changes on the break-even point-calculate the new break-even point. What lesson can we drive from this?
    i) Suppose there is no any change in fixed cost, unit variable cost and selling price, what is the maximum profit the firm can generate, and at what level of output?
    j) Keeping selling price and fixed cost constant, what is the maximum unit variable cost for the firm to break-even (at its maximum output level)?
    k) Keeping all things as they are, what is the quantity level at which the company:
    i. Makes a profit of $100,000?
    ii. Looses $10,000
    l)Had there been no capacity limitation, how would your answer have changed in part(i)?
    /please show me all the necessary steps for the solutions/
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  5. #20
    MHF Contributor MarkFL's Avatar
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    Re: Word problem: Cost function, Revenue Function, Profit function.

    You should:

    a) Begin your own topic for your question.

    b) Post 1 (or no more than 2 or 3 simple and related problems) question per topic.

    c) Post your work so far, what your thoughts are, show where you are stuck, etc.

    These are just friendly suggestions to help you get the best and most timely help.
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  6. #21
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    Re: Word problem: Cost function, Revenue Function, Profit function.

    AUDITION SONGS - 1. First verse of MAYBE (BACKING TRACK AVAILABLE )
    MAYBE FAR AWAY OR MAYBE REAL NEARBY,
    HE MAY BE POURING HER COFFEE, SHE MAYBE STRAIGHTNING HIS TIE.
    MAYBE IN A HOUSE, ALL HIDDEN BY A HILL, SHE'S SITTING PLAYING PIANO, HE'S SITTING PAYING A BILL.

    BETCHA THEY'RE YOUNG BETCHA THEY'RE SMART BET THEY COLLECT THINGS LIKE ASHTRAYS, AND ART!
    BETCHA THEY'RE GOOD — (WHY SHOULDN'T THEY BE?) THEIR ONE MISTAKE WAS GIVING UP ME!

    SO MAYBE NOW IT'S TIME, AND MAYBE WHEN I WAKE
    THEY'LL BE THERE CALLING ME "BABY" MAYBE.

    1. First verse of TOMORROW
    THE SUN'LL COME OUT, TOMORROW
    BET YOUR BOTTOM DOLLAR, THAT TOMORROW THERE'LL BE SUN!

    JUST THINKIN’ ABOUT, TOMORROW
    CLEARS AWAY THE COBWEBS, AND THE SORROW, ‘TIL THERE’S NONE!

    WHEN I’M STUCK WITH A DAY THAT’S GREY, AND LONELY,
    IJUST STICK OUT MY CHIN, AND GRIN, AND SAY, OH

    THE SUN'LL COME OUT, TOMORROW,
    SO YA GOTTA HANG ON ‘TIL TOMORROW, COME WHAT MAY

    TOMORROW! TOMORROW! I LOVE YA TOMORROW!
    YOU’RE ALWAYS A DAY AWAY!

    AUDITION DANCE
    Please demonstrate some tap steps to the song
    You're Never Fully Dressed Without A Smile


    ANNIE AUDITION SCRIPT
    Annie: Pipe down, all of you. Do you want Hannigan to hear you? I know, she’s talking in her sleep. Shhhh, Molly. It’s all right, Annie’s here. Blow. It was only a dream. Now we’ve all got to
    get back to sleep. It’s after three a.m. All right, I’ll read you my note again if you promise to go back to sleep. (clears throat) “ . . . Please take care of our little darling. We’ve named her Annie. She was born on Oct. 28 . . . “ So, you’re laughing are you? Do you want to sleep with your teeth inside your mouth or out?


    WARBUCKS (Confidently) Hello, Annie. How are you today?
    ANNIE Fine, thank you. How are you, sir?
    WARBUCKS Fine. Annie, the time has come for the two of us to have a very serious discussion.
    ANNIE You're sending me back to the Orphanage, right?
    WARBUCKS Of course not.
    WARBUCKS Annie, can we have a man-to-man
    ANNIE Sure
    WARBUCKS I was born into a very poor family in what they call Hell's Kitchen, right here in New York. Both of my parents died before I was ten and l made a promise to myself — some day, one way or another, I was going to be rich. Very rich.
    ANNIE That was a good idea.
    WARBUCKS By the time I was twenty-three I'd made my first million. Annie, do understand what I'm trying to say?
    ANNIE sure.
    WARBUCKS Good.
    ANNIE Kind of.
    WARBUCKS Kind of?
    ANNIE I guess not.
    WARBUCKS (WARBUCKS takes the Tiffany's package from his desk and hands it to ANNIE) I was in Tiffany's yesterday and picked up this thing for you. Had it engraved.
    ANNIE For me? Gee, thanks, Mr. Warbucks. You're so nice to me,
    (ANNIE opens up the package? and looks at the gift. She is clearly unhappy with it but pretends to like it.)
    ANNIE Oh. Gee.
    WARBUCKS It' s a silver locket', Annie. I noticed that old, broken one you always wear, and I said to myself I'm going to get that kid a nice new locket.
    ANNIE (Trying without much success to sound pleased) Gosh, thanks, Mr. Warbucks. Thank you very much.
    WARBUCKS (Starting to take off ANNIE's old locket) Here, we'll just take this old one off and ...
    ANNIE (Recoiling from WARBUCKS; yelling) No! No please don't make me take my locket off. I don't want a new one.
    WARBUCKS Annie, what is it?
    ANNIE (going gradually into hysterics and tears) This locket, my Mom and Dad left it with me when ... when they left me at the Orphanage. And there was a note, too. They're coming back for me. And, oh, I know, being here with you for Christmas, I'm real lucky. But ... I don't know how to say it. The one thing I want in all the world, ... more than anything else is to find my mother and father, And to be like other kids, with folks of my own.


    --------------------------------------------------------------------------------

    ORPHANS

    Orphan Character Notes

    All Children must have shoulder length hair or longer and be under 4'10''
    Molly – The smallest little girl. Should look young and be the baby. Also needs acrobatic skills
    Kate – The next smallest child. Should look seven years of age.
    Tessie – Should look ten years of age and who is the ‘cry baby’
    Pepper – Must look twelve years of age. the toughest of the orphans.
    July – Is thirteen years of age and the quietest of all the girls.
    Duffy – Thirteen years of age and the biggest of all the orphans.
    Annie – Must look eleven years of age and be a leader.
    The Eight Extra Orphans for the orphanage – who will play in the general scenes – doubling up with the gang and understudy the main named orphans need not tap.

    AUDITION SONG
    1. You¹re Never Fully Dressed Without A Smile: (BACKING TRACK AVAILABLE)
    " ...and so for all the hour of smiles..this is Bert Healy saying.."

    Hey, hobo man
    Hey, Dapper Dan
    You've both got your style
    But Brother,
    You're never fully dressed
    Without a smile!

    Your clothes may be Beau Brummelly
    They stand out a mile --
    But Brother,
    You're never fully dressed
    Without a smile!

    Who cares what they're wearing
    From Main Street,
    to Saville Row,
    It's what you wear from ear to ear
    And not from head to toe
    That matters

    AUDITION DANCE Please demonstrate some tap steps to the song
    You¹re Never Fully Dressed Without A Smile
    AUDITION MONOLOGUES Read any you like.
    Molly: Mama! Mama! Mommy! I was dreamin’ ‘bout my Mama, Annie. We was on the merry-go-round and she was smiling and holding my hand. And then, she was gone. I couldn’t stop the merry-goround and I couldn’t find her no more, no where. Annie, will you read me your note again, please? It always makes me feel better. I promise I’ll go to sleep after you read me your Note.

    Pepper: Shut up, Molly! Can’t anybody get any sleep around here? Don’t feel sorry for her. We’re the one’s who aint getting any sleep! Shut your trap, Molly! What? You’re telling me to pipe down? You must have meant that tone of voice for someone else. You wanna make somethin’ of it? You’re just beggin’ for a black eye, pal.

    Tessie: Oh my goodness, Oh my goodness! They’re fighting again and I won’t get no sleep all night! Oh my goodness, Oh my goodness! Molly’s talkin’ in her sleep. Her eyes are still closed. She don’t know how loud or soft her voice is when she’s asleep. At least she’s not snoring. Oh my goodness, oh my goodness! Now she’s snoring!


    --------------------------------------------------------------------------------

    ROOSTER, HANNIGAN & LILY
    AUDITION SONG - EASY STREET Key: Bm (BACKING TRACK AVAILABLE)

    I remember the way our sainted mother Would sit and croon us, her lullaby
    She'd say, kids, there's a place that's like no other You got to get there before you die
    You don't get there by playing from the rule book
    You stack the aces, You load the dice
    Mother dear, Oh, we know you're Down there listening - how can we follow your sweet advice to...

    Easy street, Easy street where you sleep till noon,Yeah, yeah, yeah
    She'd repeat, Easy street, better get there soon.
    Easy street, Easy street Where the rich folks play, yeah, yeah, yeah
    Move them feet to Easy street
    When you get there stay

    Hannigan can sing 'Little Girls' instead of 'Easy Street'
    Little girls Little girls Everywhere I turn I can see them
    Little girls Little girls Night and day I eat, sleep and breathe them
    I'm an ordinary woman With feelings I'd like a man to nibble on my ear
    But I'll admit no man has bit So how come I'm the mother of the year?

    Little cheeks Little teeth Everything around me is little
    If I wring Little necks Surely I will get an acquittal
    Some women are dripping with diamonds
    Some women are dripping with pearls
    Lucky me! Lucky me!
    Look at what I'm dripping with - Little girls

    How I hate Little shoes Little socks And each little bloomer
    I'd have cracked Years ago If it weren't for my Sense of humor
    Some day I'll step on their freckles Some night I'll straighten their curls
    Send a flood Send the flu Anything that You can do To little girls

    Some day I'll land in the nut house With all the nuts and the squirrels
    There I'll stay Until the prohibition of Little girls.


    AUDITION SCRIPT

    ROOSTER - Hi ya, Sis. Long time no see.
    MISS HANNIGAN - Rooster? They finally let you outta prison? What were you in for this time?
    ROOSTER - Some old geezer said I swindled him outta eleven hundred bucks.
    MISS HANNIGAN - Why’d he say that?
    LILY - Because the Rooster swindled him outta eleven hundred bucks
    ROOSTER - Sis, I’d like you to meet a friend of mine from...
    LILY - Jersey City
    MISS HANNIGAN - Rooster, do me a favor. Get outta here
    ROOSTER - So, who was the blondie I bumped into when I come in? Looked like she had a couple of dollars.
    MISS HANNIGAN - She works for Oliver Warbucks
    LILY - The Oliver Warbucks?
    MISS HANNIGAN - Annie, one of the orphans from here, is getting adopted by him.
    LILY - Crummy Orphan!
    ROOSTER - Yeah, livin’ in the lap of luxury while the two Hannigan kids ended up on the skids.

    Rooster:
    Hiya Sis. Long time no see. Yup, they finally let me out of Leavenworth. I got six months off for good behavior. You wanna know what I was in for? Ahh, some old geezer from Yonkers said I swindled him out of 11 hundred bucks. Ya know why he said that? Because the Rooster swindled him outta 11 hundred bucks! Sis, I’d like you to meet a friend of mine from . . . Jersey city. Miss Lily St. Regis. Whatdaya think, sis? She’s named after the hotel. (chuckles) No, I’m not sure which floor.

    Lily:
    Why did the old geezer from Yonkers say that the Rooster Swindled him outta 11 hundred bucks? Because he swindled Him outta 11 hundred bucks. I’m Lily St. Regis from Jersey City. You know, like the hotel. I’m named after it! So you live in this dump? The city may foot your bill but This aint exactly Buckingham Palace. Your pearls aint even Real. Rooster, I thought you said your big sis was livin’ in Clover? She’s livin’ in the skids.

    Hannigan:
    Ah ha! Caught ya! I hear ya! I always hear ya! Get Up! All of ya! Well, is this the way you say good-Morning? I know it’s 4 O’ clock in the morning. That’s Your problem. Now what do you say? W h a t d o y o u S a y ? Tell me how much you love me. Rotten orphans! You kids in here, get up! Put them things away. For this One’s shenanigans you’ll scrub the floors and strip them beds for the laundry man. Rise and shine!


    --------------------------------------------------------------------------------

    WARBUCKS, GRACE
    AUDITION SONG - NYC (BACKING TRACK AVAILABLE) Key. Bb

    NYC, what is it about you, you're big, you're loud, you're tough
    NYC, I go years without you then I can't get enough
    Enough of the cab drivers answering back in language far from pure
    Enough of frankfurters answering back, oh brother, you know you're in
    NYC, too busy, too crazy, too hot, too cold, too late, I'm sold again on NYC

    NYC The shadows at sundown, the roofs that scrape the sky
    NYC the rich and the rundown, the big parade goes by
    What other town has the Empire State and a mayor five foot two
    No other town in the whole forty eight can half compare to you
    Oh NYC You make 'em all postcards
    You crowd, you cramp, you're still the champ Amen For NYC,

    AUDITION SCRIPTS

    Warbucks, Grace,

    WARBUCKS And, Grace, if you’ll get your notebook...Who is that”
    GRACE This is Annie, Mr. Warbucks: the orphan who will be with us for Christmas.
    WARBUCKS That’s not a boy. Orphans are boys.
    GRACE I’m sorry, sir, you just said “orphan”. So, I chose a girl.
    WARBUCKS Well, I suppose she’ll have to do. (Frowningly approaching ANNIE, assessing her) Annie, huh? Annie what?
    ANNIE Oh. I’m just Annie, Mr. Warbucks, sir. I haven’t got any last name. I’m sorry I’m not a boy.
    WARBUCKS (Obviously not meaning it) Not at all. I couldn’t be happier. Grace, we’ll start with the figures on the iron-ore shipments from Toledo to... (Made uncomfortable by the presence of ANNIE, aside to GRACE) What are we supposed to do with this child?
    GRACE (Aside to WARBUCKS) It is her first night here, sir
    WARBUCKS (Aside to GRACE) Hmmm (to ANNIE) Well, Annie, I guess we ought to do something special on your first night. (Has an idea) Would you like to go to a movie?
    ANNIE (Checking GRACE to see if this would be all right; GRACE nods) Gosh, Mr. Warbucks, I’ve never been to one
    WARBUCKS Then you’ll go to the Roxy. And then an ice-cream soda at Rumplemayer’s and an hansom cab ride around Central Park.
    ANNIE Golly.
    WARBUCKS Grace, forget about the dictation for tonight. Instead, you take Annie to the movies.
    GRACE Yes, sir
    ANNIE (Obviously disappointed about something) Aw, gee.
    WARBUCKS Something the matter, Annie?
    ANNIE It’s just that...well...I thought you were going to take me.
    WARBUCKS Oh, no, I’m afraid I’ll be far too busy tonight.
    ANNIE Aw, gee.
    WARBUCKS Now, Annie...I’ve just been away for six weeks. And when a man is running a multi-billiondollar
    corportation...
    ANNIE Oh, sure. I know. That’s okay, Mr. Warbucks.

    Warbucks:
    Been away six weeks, where is everybody? Hello! It’s good to be home. The flight wasn’t bad. It took eleven hours and we only had to land four times. Now, first thing’s first. Has the painting arrived from Paris? Let me see it before they hang it. Ah, yes. Hmm? No, I don’t think so. Any messages? The president. I’ll get back to him tomorrow. Anyone else? All right,
    good to see you all again. Grace, if you’ll get your notebook and - - Who is that? The orphan? But that’s not a boy. orphans are supposed to be boys.

    Grace:
    Good afternoon, Miss Hannigan is it? Oh, good. I’m Grace Farrell and the New York City board of orphans suggested that I . . . Miss Hannigan, I’m sorry but I don’t have the slightest idea about this run-away that you’re talking about. I’m not peddling anything. I’m the private secretary to Oliver Warbucks. Mr. Warbucks has decided to invite an orphan to spend the Christmas holidays at his home. I’m here to select one.


    --------------------------------------------------------------------------------

    BERT HEALY - RADIO PRESENTER

    1. You¹re Never Fully Dressed Without A Smile: (BACKING TRACK AVAILABLE)

    Hey, hobo man
    Hey, Dapper Dan
    You've both got your style
    But Brother,
    You're never fully dressed
    Without a smile!

    Your clothes may be Beau Brummelly
    They stand out a mile --
    But Brother,
    You're never fully dressed
    Without a smile!

    Who cares what they're wearing
    From Main Street,
    to Saville Row,
    It's what you wear from ear to ear
    And not from head to toe
    That matters

    Healy (unctuous) Thank you, Annie. Thank you, Annie. On America’s favourite radio program, the Oxydent hour of Smiles, starring your old softy, Bert Healy. Say, Wacky, who’s that who just walked into our WEAF studio? Wacky Why it’s none other than that wealthy industrialist and Wall St. tycoon, Oliver Warbucks. Now, Oliver Warbucks, I understand that you are now conducting a coast-to-coast nation-wide search for Annie’s parents and offering a certified check for $50,000 dollars to any persons who can prove that they are Annie’s parents. Wow! So Annie’s parents, if you’re listenin’ in, write to Oliver Warbucks care of this Station, WEAF, New York, or directly to him at… 987 Fifth Avenue, New York, New York. That’s 987 Fifth Avenue, New York, New York. Goodnight, Oliver Warbucks. (Applause sign) Thanks for dropping by, Oliver Warbucks. So, Annie’s parents, if you’re listenin’ in, there’s $50,000 and a wonderful daughter waiting for you. So get in touch right away, ya hear?

    CHORUS
    AUDITION SONG - Sing any song from the show or a song of your own choice. (I will have the accompaniments for the Annie songs but bring your own music if you sing a song of your own choice. Make sure the music is taped together and sight-readable. You can use backing tracks if you want to. Don't attempt to sing unaccompanied!)

    DANCERS Demonstrate any dance ability
    SPEAKING VOICE

    Parts to be cast are Radio Show Fred McCracken (ventriloquist male or female) & Wacky a small child playing the Dummy.


    FRED Smile, darn ya, smile.
    Wacky Smile, darn ya, smile. (Sound effects man creates sound of a door opening & closing and then of feet across the studio)
    FRED Say, Wacky, who’s that who just walked into our WEAF studio?
    Wacky Why it’s none other than that wealthy industrialist and Wall St. tycoon, Oliver Warbucks. (Applause sign)
    FRED Now, Oliver Warbucks, I understand that you have something to tell the folks at home about wonderful little Annie here.
    WARBUCKS Yes, Bert Healy, I am now conducting a coast-to-coast nationwide search for Annie’s Parents.
    Wacky Wow! Oh boy-oh boy-oh-boy, 50,000 smackers!
    FRED Wow! So Annie’s parents, if you’re listenin’ in, write to Oliver Warbucks care of this Station, WEAF, New York,
    Wacky And I would also like to take this opportunity to thank the makers of all-new Oxydent toothpaste, with miracle L-64 to fight bad breath, for letting me appear here this evening.

    BUNDLES McCLOSKEY - The Laundryman (could be female) & Police officers Boy: I got him! I got the dog! Now what should we do with him? The dog Catcher said he was dangerous. He don’t look dangerous to me. He’s just a dumb mutt, that’s all. He aint worth nothin’. Maybe We should shoot him. We’d be town heroes! Hey, I know what we could do with him. (with a mischievous grin) As long as we don’t Get caught . . .

    Boy 2. Stew again? We had stew last night – and the night before. There wasn’t any meat in it. I know, beggers can’t be choosers. Will you look at this? We made the papers again. “...In Hoover they trusted and now they are busted...” The story of Our lives. “ ... thousands of once affluent Americans are today Living in makeshift towns known as Hoovervilles...” It says here that in New York City
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