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Question 1141943: Formulate but do not solve the following exercise as a linear programming problem.
A hunger-relief organization has earmarked between $2 million and $3.5 million (inclusive) for aid to two African countries, Country A and Country B. Country A is to receive between $1 million and $1.75 million (inclusive), and Country B is to receive at least $0.25 million. It has been estimated that each dollar spent in Country A will yield an effective return of $0.40, whereas a dollar spent in Country B will yield an effective return of $0.70. How should the aid be allocated if the money, in millions, is to be utilized most effectively according to these criteria?
Hint: If x and y denote the amount of money, in millions of dollars, to be given to Country A and Country B, respectively, then the objective function to be maximized is
P = 0.4x + 0.7y.
max amount both countries receive collectively x + y ≤
min amount both countries receive collectively x + y ≥
max amount Country A receives x ≤
min amount Country A receives x ≥
min amount Country B receives y ≥
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! x = the amount of money invested in country A
y = the amount of money invested in country B
your objective function is p = .4 * x + .7 * y
your constraints are:
total money is between 2 million and 3.5 million.
x + y >= 2
x + y <= 3.5
country A is to receive between 1 and 1.75 million.
x >= 1
x <= 1.75
country B is to receive at least .25 million.
y >= .25
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