# A manufacturing firm produces electric motors for washing machines and vacuum cleaners. The firm …

A manufacturing firm produces electric motors for washing machines and vacuum cleaners. The firm has resource constraints for production time, steel, and wire. The linear programming model for determining the number of washing machine motors (x1) and vacuum cleaner motors (x2) to produce that would maximize the profit has been formulated as follows:

ANSWER LETTERS A THROUGH E IN SEQUENTIAL ORDER!

A. Formulate the dual for this problem.

B. What do the dual variables equal, and what do they mean?

C. Determine the sensitivity range for the profit from washing machine motors (c1) using the optimal tableau. Show your work!

D. Determine the feasible range for production hours (q1) and pounds of steel (q2) using the optimal tableau. Show your work!

E. What are the values of resources (production time, steel, and wire) that are utilized to produce (1) one washing machine motor, (2) one vacuum cleaner motor?

30 x1 40 x maximize str 2×1 3×2 s 12 (production time) x1 4×2 s 12 (steel) 2×1 2×2 10 (wire) x1,x2 2 0 The final optimal simplex tableau for this model is as follows: 30 40 Basic Cj Variables Quantity X1 X2 S1 S2 30 4.5 x1 0.25 40 0.5 x2 3.5 s2 1.75 30 40 175 12.5 12.5 S3 0.75 0.5 1.25 2.5 -2.5