Chapter 3.2, Problem 20E

SOCIAL PROGRAMS PLANNING AntiFam a hunger-relief organization, has earmarked between $\$2\text{million}$ and $\$2.5\text{million}$ (inclusive) for aid to two African countries, Country A and Country B. Country A is to receive between $\$1\text{million}$ and $\$1.5\text{million}$ (inclusive), and Country B is to receive at least $\$0.75\text{million}$. It has been estimated that each dollar spent in Country A will yield an effective return of $\$0.60$, whereas a dollar spent in Country B will yield an effective return of $\$0.80$. How should the aid be allocated if the money is to be utilized most effectively according to these criteria?

Hint: If x and y denote the amount of money to be given to Country A and Country B, respectively, then the objective function to be maximized is $P=0.6x\text{+0}\text{.8}y$.