Chapter 6.4, Problem 42E

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

Trail mix. A company makes two brands of trail mix, regular and deluxe, by mixing dried fruits, nuts, and cereal. The recipes for the mixes are given in the table. The company has $1,200$ pounds of dried fruits, $750$ pounds of nuts, and $1,500$ pounds of cereal for the mixes. The company makes a profit of $\text{\$}0.40$ on each pound of regular mix and $\text{\$}0.70$ on each pound of deluxe mix. How many pounds of each ingredient should be used in each mix in order to maximize the company’s profit?