AntiFam, a hunger-relief organization has earmarked between $2 and $2.5 million (inclusive) for aid to two African countries, country A and country B. Country A is to receive between $1 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 $.60, where a dollar spent in country B will yield an effective return of $.80. How should the aid be allocated if the money is to be utilized most effectively according to the these criteria.
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=.6x +.8y.
a. Identify your variables.
b. Set up the objective and constraints.
c. Graph the feasible region.
d. Determine the corner points. Show the algebra if solving for the intersection of lines.
e. Determine the optimal solution and report you results in terms of the names of the variables.