Dean's Furniture Company assembles regular and deluxe kitchen cabinets from precut lumber. The regular cabinets are painted white, and the deluxe are varnished. Both painting and varnishing are carried out in one department. The daily capacity of the assembly department is 200 regular cabinets and 150 deluxe. Varnishing a deluxe unit takes twice as much time as painting a regular one. If the painting/varnishing department is dedicated to the deluxe units only, it can complete 180 units daily. The company estimates that the revenues per unit for the regular and deluxe cabinets are $100 and $140, respectively.

(a) Formulate the problem as a linear program and find the optimal production schedule per day.

(b) Suppose that competition dictates that the price per unit of each of regular and deluxe cabinets be reduced to $80. Use sensitivity analysis to determine whether or not the optimum solution in (a) remains unchanged.