Chapter 5.3, Problem 42E

In Problems 49-64, construct a mathematical model in the form of a linear programming problem. (The answers in the back of the book for these application problems include the model.) Then solve by the geometric method.

Computers. An electronics firm manufactures two types of personal computers––a standard model and a portable model. The production of a standard computer requires a capital expenditure of $\text{\$}400$ and $40$ hours of labor. The production of a portable computer requires a capital expenditure of $\text{\$}250$ and $30$ hours of labor. The firm has $\text{\$}20,000$ capital and $2,160$ labor-hours available for production of standard and portable computers.

(A) What is the maximum number of computers the company is capable of producing?

(B) If each standard computer contributes a profit of $\text{\$}320$ and each portable model contributes a profit of $\text{\$}220$, how much profit will the company make by producing the maximum number of computers determined in part (A)? Is this the maximum profit? If not, what is the maximum profit?