need help with min/max word problems plz, someone help, i dont get this at all

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October 3rd 2007, 04:40 PM
kuttaman

need help with min/max word problems plz, someone help, i dont get this at all

my teacher is giving these word problems, and i am not getting them, the problems is not solving them, problem is the let statements, how to create them, what keywords to look for, and how to create an equation essentially solving is no problem plz help, test on friday,

some example of questions are
a farmer wants a rectangular field with 180m of fenching, what are the dimensions of the field if the area is to be a maximum?

Tow numbers have a sum of 36, find the number if the sum of theri squares is a minumium and state the minimum

a theathre group presently charges $12 to see a play, for each 2$ increase in the ticket price, the group figures it will lose 100 pators, the theathre can hold 1200 people,

what is the maximum possible revenue, what ticket price produces the maximum, how many patrons are neeed to provide this maximum revenue.

Assume that a jogger burns callories at a rate given by B= -3/2v^2 + 48v +561 for 0< v <30

B is calories burned per hour and v is the joggers speeed in km/h

what is the maxmimum number of calories that can be burned per hour?, at what speeed is the maximum achieved.

THERE are alot more, but help with these will be greatly appreciated. ty
October 3rd 2007, 04:49 PM
topsquark

Quote:

Originally Posted by kuttaman

a farmer wants a rectangular field with 180m of fenching, what are the dimensions of the field if the area is to be a maximum?

Here is more or less my method of attack:

Look in the problem statement for possible equations you could use. In this case we have a rectangle mentioned and the perimeter and area of it. So write down the equations:
$P = 2l + 2w$
and
$A = lw$
where l is the length of the rectangle and w is the width.

You know that P = 180 m, so
$180 = 2l + 2w$

We wish to maximize the area, so we need to find a value of l in terms of w (or the other way around). The obvious way to do this is:
$l = \frac{180 - 2w}{2} = 90 - w$

So
$A = (90 - w)w = 90w - w^2$

Now find the w that maximizes the area.

-Dan
October 3rd 2007, 04:52 PM
topsquark

Quote:

Originally Posted by kuttaman

Two numbers have a sum of 36, find the number if the sum of their squares is a minumium and state the minimum.

Again I look for equations.

"Two numbers have a sum of 36"
So label one number as x and the other as y and we get:
$x + y = 36$

We want the sum of the squares of x and y to be a minimum.

So we wish to minimize $z = x^2 + y^2$ .

Again we can use the first equation to get rid of one of the variables:
$y = 36 - x$

So we minimize:
$z = x^2 + (36 - x)^2$

etc.

-Dan
October 3rd 2007, 05:05 PM
kuttaman

???/

dude im not getting this. can u help me fiure out how to set equations
October 3rd 2007, 05:08 PM
topsquark

Quote:

Originally Posted by kuttaman

dude im not getting this. can u help me fiure out how to set equations

Without sitting down in front of you and working this out I'm not sure how much I can help you.

The basic idea in setting up a word problem is to find quantities to label and use the problem to set up equations for you. I can give you examples, but little help without knowing how you are approaching this. (And this process can be very difficult over the computer.)

You appear to be in a Calculus class? If you are having significant difficulties with setting up word problems at this level I would suggest either a personal tutor or arranging time with your teacher to go over this topic.

-Dan
October 3rd 2007, 05:22 PM
kuttaman

yea i understand what u mean

problem is my teacher just came out of retirement so he cant explain it to me properly, and my class is advanced functions grade 11, not at calc yet anyways thx for help