Linear Programming

[Batarang96]

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

A hunger-relief organization has earmarked between $2 million and $2.5 million (inclusive) for aid to two African countries, Country A and Country B. Country A is to receive between $1 million and $1.25 million (inclusive), and Country B is to receive at least $0.5 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 return of $0.80. 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=.5x+.8y

I need to complete the constraints below:

x+y

≤​

x + y

≥

x

≤

x

≥
​

y

≥​

Thanks in advance.

 

[ksdhart]

Okay, so you need to set up constraints for the problem. A lot of the work has already been done by somebody, because the relevant values are highlighted in red, you just need to determine which one to put where. Let's look at the constraints you have...

x + y <= ? and x + y >= ?
In the hint, you're told that x and y represent the amount of money given to country A and country B, respectively. So, then what does x+y represent? You're being asked to find the maximum possible value of x+y, so which of the values from the problem would you choose? The second one is the same as the first, except instead you're looking for the minimum possible value of x+y. What is that amount?

x <= ? and x >= ?

Okay, so you're trying to find the minimum possible value of just x? What does the problem say is the maximum possible amount to be given to country A? And the minimum possible amount?

y >= ?

The problem does not given a maximum amount to give country B, but it does give a minimum. What is that amount?