Formulate and use linear programming to solve the following problem. A firm wants to determine how many units of each of two products (products D and E) they should produce to make the most money. The profit in the manufacture of a unit of product D is $100 and the profit in the manufacture of a unit of product E is $87. Although the firm can readily sell any amount of either product, it is limited by its total labor hours and total machine hours available. The total labor hours per week are 4,000. Product D takes 5 hours of labor per unit and product E takes 7 hours of labor per unit. The total machine hours are 5,000 per week. Product D takes 9 hours of machine time per unit and product E takes 3 hours of machine time per unit. Write the constraints and the objective function for this problem, solve for the best mix of product D and E, and report the maximum value of the objective function. Objective function: Maximize Z = $100 D + $87 E Subject to constraints: 5 D + 7 E < = 4,000 9 D + 3 E < = 5,000 Solution: D = 479.17 E = 229.17 Z = $67,854