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Need help in setting up constrained functions

  1. Oct 26, 2007 #1
    [SOLVED] Need help in setting up constrained functions

    I'm studying linear programing and I need some help on writing the constrained functions. This particular problem is hard because there is more than 1 unknown. The variables are bolded.
    1. The problem statement, all variables and given/known data
    Each quart of the regular cream that John makes contains 2 cups of waterand 1 cup of cocoa butter. Each quart of his extra rich cream contains 1 cup of waterand 2 cups of cocoa butter. John makes $10 profits on each quart of the regular cream and an $8 profit on each quart of the extra rich cream. If he has 12 cups of water and 8 cups of cocoa butter on hand, how many quarts of each type of cream should he make to maximize his profits.

    2. Relevant equations
    Write the constrained functions to graph and figure out the number of quarts of each type of cream that he should make to maximize his profits
    3. The attempt at a solution
    Constrained functions:
    water=X; cocoa butter=y
    2x+1y <12; which is y<10-2X
    1x+2y<8, which is y< 4-.5x
    x>0
    y>0
    Objective function to plug in the coordinate:
    10X+8Y
     
    Last edited: Oct 26, 2007
  2. jcsd
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