A company imports electronic components that are used to assemble two different types of computer modules for tractors. One model, A, generates a profit contribution of $50 per unit whereas the other, B, generates a profit contribution of $40 per unit. For next week's production, a maximum of 150 hours (b1) of assembly time can be made available. Each unit of A requires three hours of assembly time, and each unit of B requires five hours. In addition, the company currently has in inventory 20 dis- play units used in B; thus, no more than 20 units of B can be assembled. Finally, only 300 (b2) square meters of warehouse space can be made available next week. Each unit of A requires eight square meters, and each unit of B requires five square meters.

a. Construct an LP problem to find the optimal production for next week to maxi- mize profit.

b. Find the dual of the LP problem from part a.

c. Solve either the primal or the dual problem using the simplex method.

d. Calculate the range of feasibility for b1.

e. Calculate the range of optimality for the profit contribution of part a.