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 company
Product A: Profit=$500, Cost=$200
Product B: Profit=$400, Cost= $150
If 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 $200,000

Required:

Formulate Objective Function, Assembly Hours Constraint, Labor Hours Constraint, and Desired Profitability Equation.