Chapter 6.4, Problem 39E

In Problems 39-47, construct a mathematical model in the form of a linear programming problem. Do not solve.

Manufacturing. A company manufactures car and truck frames at plants in Milwaukee and Racine. The Milwaukee plant has a daily operating budget of $\text{\$}50,000$ and can produce at most $300$ frames daily in any combination. It costs $\text{\$}150$ to manufacture a car frame and $\text{\$}200$ to manufacture a truck frame at the Milwaukee plant. The Racine plant has a daily operating budget of $\text{\$}35,000$, and can produce a maximum combined total of $200$ frames daily. It costs $\text{\$}135$ to manufacture a car frame and $\text{\$}180$ to manufacture a truck frame at the Racine plant. Based on past demand, the company wants to limit production to a maximum of $250$ car frames and $350$ truck frames per day. If the company realizes a profit of $\text{\$}50$ on each car frame and $\text{\$}70$ on each truck frame, how many frames of each type should be produced at each plant to maximize the daily profit?