Chapter 5.3, Problem 58E

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.

Capital expansion. A fast-food chain plans to expand by opening several new restaurants. The chain operates two types of restaurants, drive-through and full-service. A drive-through restaurant costs $\text{\$}100,000$ to construct, requires $5$ employees, and has an expected annual revenue of $\text{\$}200,000$. A full-service restaurant costs $\text{\$}150,000$ to construct, requires $15$ employees, and has an expected annual revenue of $\text{\$}500,000$. The chain has $\text{\$}2,400,000$ in capital available for expansion. Labor contracts require that they hire no more than $210$ employees, and licensing restrictions require that they open no more than $20$ new restaurants. How many restaurants of each type should the chain open in order to maximize the expected revenue? What is the maximum expected revenue? How much of their capital will they use and how many employees will they hire?