Formulate and use linear programming to solve the following problem (the only difference from the previous problem is that an additional 100 hours of labor is now available). A firm wants to determine how many units of each of three products (products X, Y, and Z) they should produce in order to make the most money. The profit from making a unit of product X is $130, the profit from making a unit of product Y is $80, and the profit from making a unit of product Z is $70. Although the firm can readily sell any amount of each of the products, it is limited by its total labor hours and total machine hours available. The total labor hours per week are 1200. Product X takes 5 hours of labor per unit, product Y takes 2 hours of labor per unit, and product Z takes 2 hours of labor per unit. The total machine hours available are 1250 per week. Product X takes 2 machine hour per unit, product Y takes 4 machine hours per unit, and product Z takes 2 machine hours per unit. Write the constraints and the objective function for this problem, solve for the best mix of product X, Y, and Z, and report the maximum value of the objective function.
In the solution, what is the value of the objective function?