Formulate but do not solve the following exercise as a linear programming proble

Question

Formulate but do not solve the following exercise as a linear programming problem. A hunger-relief organization has earmarked between $2 million and $4 million (inclusive) for aid to two African countries, Country A and Country B. Country A is to receive between $1 million and $1.5 million (inclusive), and Country B is to receive at least $0.75 million. It has been estimated that each dollar spent in Country A will yield an effective return of $0.50, whereas a dollar spent in Country B will yield an effective returns of $0.60. How should the aid be allocated if the money, in millions, is to be utilized most effectively according to these criteria? max amount both countries receive collectively x + y lessthanorequalto min amount both countries receive collectively x + y greaterthanorequalto max amount Country A receives x lessthanorequalto min amount Country A receives x greaterthanorequalto min amount Country B receives y greaterthanorequalto

Explanation / Answer

The total budget allotted for relief is between $ 2 million and $ 4 million. Thus if x were to represent the amount of funding given to country A and y represent the funding given to country B, then we have the following constraints based on the budget restrictions,

x + y <= $ 4 million

x+ y >= $ 2 million

There is also individual fund allocation restriction on the countries.Country A's funding lies in between

$ 1 million and $ 1.5 million. And country B's funding has been has a floor of $ 0.75 million.

Writing out the constraints, we get

x <= $ 1.5 million

x >= $ 1 million

y >= $ 0.75 million

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