Results 1 to 3 of 3

Math Help - Graphical Method Word Problems

  1. #1
    Newbie
    Joined
    Mar 2013
    From
    Canada
    Posts
    5

    Graphical Method Word Problems

    1)The loan department in a bank will use at most $25 million or commercial and home loans. The bank's policy is to allocate at least four times as much money to home as to commercial loans. The bank's return is 12% on a home loan and 10% on a commercial loan. The manager of the loan department wants a return of at-least $2.8 million on these loans. Let x be the amount of home loans and y for the amount for commercial loans.

    (a) Write a system of inequalities that describes the above conditions
    (b) Graph the corresponding feasible region

    2) Consider the situation of a small brewery whose ale and beer are always in demand but whose production is limited by a certain raw materials that are short in supply. Suppose the scarce ingredients are corn, hops and barely malt. To make one barrel of ale requires 5 pounds of corn, 4 ounces of hop, and 35 pounds of barley malt. To make a barrel of beer requires 15 pounds of corn, 4 ounces of hop and 20 pounds of barley malt. Suppose that 480 pounds of corn, 160 ounces of hop and 20 pounds of barley malt are available.

    If each brewery of ale yields a profit of $13 and each barrel of beer yields $23 profit, how can the brewery maximize its total profit?
    Last edited by NateDawg; March 13th 2013 at 08:28 AM.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Apr 2005
    Posts
    15,583
    Thanks
    1418

    Re: Graphical Method Word Problems

    Quote Originally Posted by NateDawg View Post
    1)The loan department in a bank will use at most $25 million or commercial and home loans. The bank's policy is to allocate at least four items as much money to home as to commercial loans.
    I don't understand this. What "four items"? Do you mean "four times as much money"? I'm going to assume that.

    The bank's return is 12% on a home loan and 10% on a commercial loan. The manager of the loan department wants a return of at-least $2.8 million on these loans. Let x be the amount of home loans and y for the amount for commercial loans.

    (a) Write a system of inequalities that describes the above conditions
    "The bank's policy is to allocate at least four times as much money to home as to commercial loans." So x\ge 4y.
    "The manager of the loan department wants a return of at-least $2.8 million on these loans." I assume this is "per year". The return on loans of x dollars at 12% interest is .12x. The return on loans of y dollars at 10% interest is .10y. The total is .12x+ .10y\ge 2800000

    (b) Graph the corresponding feasible region
    You also have, of course, x\ge 0 and y\ge 0. To find the boundary of the feasible region replace each inequality sign by and equals sign and graph the resulting line.

    2) Consider the situation of a small brewery whose ale and beer are always in demand but whose production is limited by a certain raw materials that are short in supply. Suppose the scarce ingredients are corn, hops and barely malt. To make one barrel of ale requires 5 pounds of corn, 4 ounces of hop, and 20 pounds of barley malt. Suppose that 480 pounds of corn, 160 ounces of hop and 20 pounds of barley malt are available.

    If each brewery of ale yields a profit of $13 and each barrel of beer yields $23 profit, how can the brewery maximize its total profit?
    You seem to have left out important information- "To make one barrel of ale requires 5 pounds of corn, 4 ounces of hop, and 20 pounds of barley malt" but how much is required to make a barrel of beer?
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Mar 2013
    From
    Canada
    Posts
    5

    Re: Graphical Method Word Problems

    Edited to reflect corrections
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Counting Problems Math Help-3 word problems
    Posted in the Statistics Forum
    Replies: 9
    Last Post: November 15th 2012, 07:30 PM
  2. Game Theory - graphical method
    Posted in the Statistics Forum
    Replies: 0
    Last Post: May 13th 2012, 01:06 AM
  3. Logic Word Problems-need a faster method!
    Posted in the Algebra Forum
    Replies: 1
    Last Post: December 4th 2008, 10:34 PM
  4. graphical method?
    Posted in the Pre-Calculus Forum
    Replies: 1
    Last Post: October 9th 2008, 02:06 PM
  5. Replies: 1
    Last Post: September 29th 2008, 08:38 AM

Search Tags


/mathhelpforum @mathhelpforum