Question

A computer parts manufacturer produces two types of monitors—monochrome and color. There are two production lines, one for each type of monitor. The monochrome monitor line has a daily capacity of 700 units per day. The color monitor line has a daily capacity of 500 units per day. In department A, the LCD panels are produced for both monitor lines. In department A, the production of monochrome LCD requires one hour of labor, and a color monitor requires two hours of labor. Total daily labor hours in department A is 1,200 hours. In department B, the monitors are inspected. The monochrome monitor requires 3 hours of labor for inspection. The color monitor requires 2 hours of labor for inspection. A total of 2,400 hours of labor are available in department B. The monochrome monitor nets an earnings contribution of $40 per unit. The color monitor nets an earnings contribution of $30 per unit.

(a) (5 points) By using two decision variables M and C, formulate a linear programming problem. (M is the daily production of monochrome monitors in hundreds of monitors, and C is the daily production of color monitors in hundreds of monitors.)

(b) (10 points) Solve the linear programming model graphically. Show each constraint, the feasible region, and identify the optimal solution.

(c) (5 points) Which two constraints are binding at the optimal solution? Solve these two constraints with the two unknowns to compute the optimal production plan exactly.

(d) (5 points) Compute the shadow price of the constraint for department A.

(e) (5 points) Assume that we can increase the labor hours of department A by ∆ (i.e., 1200 hours → 1200 + ∆ hours). Calculate the range of ∆ that maintains the optimal solution.

(f) (5 points) Assume that the net earnings contribution of the monochrome monitor can be changed by δ (i.e., $40 → $40 + δ). Calculate the range of δ that maintains the optimal solution.

Expert Answer

Answer 1

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