Chapter 12.1, Problem 24E

In Exercises $21-24$, the region of possible solutions is not bounded: thus, there may not be both a maximum and a minimum. After graphing the region of possible solutions and finding each corner point, you can determine if both a maximum and a minimum exist by choosing two arbitrary values of $z$ and graphing the corresponding lines, as discussed in the section “Why the Corner Principle Works.”

Eaton’s Chocolates produces semisweet chocolate chips and milk chocolate chips at its plants in Bay City and Estancia. The Bay City plant produces $3,000$ pounds of semisweet chips and $2,000$ pounds of milk chocolates chips each day at cost of $\$1,000$, while the Estancia plant produces $1,000$ pounds of semisweet chips and $6,000$ pounds of milk chocolates chips each day at cost of $\$1,500$. Eaton’s has an order from SafeNShop Supermarkets for at least $30,000$ pounds of semisweet chips and $60,000$ pounds of milk chocolates chips. How should it schedule its production so that it can fill the order at minimum cost? What is that minimum cost?