1. Bus, Inc. produces 2 products, A and B, each requiring direct material and labor. Product A sells for $10 each and Product B sells for $15 each. It takes workers 3 hours to make a unit of A and 1 hour to make a unit of B. It takes 2 pounds of materials to make a unit of A and 4 pounds to make a unit of B. Total labor available is 200 hours; total material available is 300 pounds. The variable costs associated with each unit of A are $6 and the variable costs associated with each unit of B are $10. A manager at Bus is setting up a linear programming model to determine the optimal production mix.

a. Write out the objective function and the constraints for the problem.

b. Graph and label the constraints, clearly denoting the feasible production set on your graph.

c. What is the value of the objective function at the intersection point of the constraints, and the two intercepts? What is the optimal production mix?