1. Formulate and use linear programming to solve the following problem. A company wants to determine how many units of each of two products (products X and Y) it must produce to make the most money. The profit from making one unit of product X is $100 and the profit from making one unit of product Y is $80. Although the company can easily sell any quantity of either product, it is limited by the total labor hours and total machine hours available. The total work hours per week is 800. Product X requires 4 work hours per unit and Product Y requires 2 work hours per unit. 
2. 
   
3. The total available machine hours is 750 per week. Product X takes 1 machine hour per unit and Product Y takes 5 machine hours per unit. 
4. Write the constraints and the objective function for this problem, solve for the best combination of products X and Y, and report the maximum value of the objective function.