1. Apply linear programming to this 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 $300 and the profit in the manufacture of a unit of product E is $97. The firm is limited by its total available labor hours and total available machine hours. The total labor hours per week are 3,000. Product D takes 6 hours per unit of labor and product E takes 8 hours per unit. The total machine hours are 4,000 per week. Product D takes 10 hours per unit of machine time and product E takes 4 hours per unit.Required:Write objective function and labor hours and machine hours constraints.2. There are two products of a companyProduct A: Profit=$500, Cost=$200Product B: Profit=$400, Cost= $150If labor hrs. are 1000, product A requires 5 labor hrs, and product B requires 7 labor hrs.If Assembly hrs. are 1500, product A requires 10 assembly hrs, and product B requires 15 assembly hrs.If profit is at least $200,000Required:Formulate Objective Function, Assembly Hours Constraint, Labor Hours Constraint, and Desired Profitability Equation.
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