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 $0.40 on each pound of regular mix and $0.60 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?

In Problem, construct a mathematical model in the form of a linear programming problem.

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Type of Mix Regular Ingredients At least 20% nuts At most 40% cereal At least 30% nuts At most 25% cereal Deluxe