Formulate and solve the following linear program. A firm wants to determine how many units of each of two products (Xerta and Yokum) they should produce in order to make the most money. The profit from making a unit of product X is $100 and the profit from making a unit of product Y is $80. Although the firm can readily sell any amount of either product, it is limited by its total labor and machine hours available. The total labor hours per week are 800. Product X takes 4 hours of labor per unit and Product Y takes 2 hours of labor per unit. The total machine hours available are 750 per week. Product X takes 1 machine hour per unit and Product Y takes 5 machine hours per unit. Graph the functions and determine the feasible region. What is the best mix of products X and Y to maximize profit? What is the maximum value of the objective function?
Maximize Z = $100 X + $80 Y
4 X + 2 Y £ 800
1 X + 5 Y £ 750
X, Y > 0