The Flair Furniture Company first described in Chapter 7, and again in this chapter, manufactures inexpensive tables (T) and chairs (C). The firm’s daily LP formulation is given as

Maximize profits = 70T + 50C

subject to 4T + 3C ≤ 240 hours of carpentry time available

2T + 1C ≤ 100 hours of painting time available

In addition, Flair finds that three more constraints are in order. First, each table and chair must be inspected and may need reworking. The following constraint describes the time required on the average for each:

0.5T + 0.6C ≤ 36 hours of inspection/rework time available

Second, Flair faces a resource constraint relating to the lumber needed for each table or chair and the amount available each day:

32T + 10C ≤ 1,248 linear feet of lumber available for production

Finally, the demand for tables is found to be a maximum of 40 daily. There are no similar constraints regarding chairs.

T ≤ 40 maximize table production daily

These data have been entered in the QM for Windows software that is available with this book. The inputs and results are shown in the accompanying printout. Refer to the computer output in Programs M7.1A, M7.1B, and M7.1C in answering these questions.

(a) How many tables and chairs should Flair Furniture produce daily? What is the profit generated by this solution?

(b) Will Flair use all of its resources to their limits each day? Be specific in explaining your answer.

(c) Explain the physical meaning of each shadow price.

(d) Should Flair purchase more lumber if it is available at $0.07 per linear foot? Should it hire more carpenters at $12.75 per hour?
(e) Flair’s owner has been approached by a friend whose company would like to use several hours in the painting facility every day. Should Flair sell time to the other firm? If so, how much? Explain.
(f) What is the range within which the carpentry hours, painting hours, and inspection/rework hours can fluctuate before the optimal solution changes?
(g) Within what range for the current solution can the profit contribution of tables and chairschange?

Transcribed Image Text:

Eile Edit Vew Module Format Tools Window Help Objective This cel cen not be charged RHS 50 Maximize Carpentry hours Painting hours Inspection hours Lumber (linear feet) Demand 70 240 100 36 1248 40 0.6 0.5 32 Iterations Cj teration 3 Basic Variables Flair Furniture Solution 50 C slack slack 2 slack 3 slack 4slack Quantity 70 slack 1 slack 2 03.9437-0.0634 1-0.8451-0.0493 0 2.2535 0.0352 00.7042 0,0423 0 0.7042 -0.0423 0 63.3803 1.1972 1.1972 0 18.9296 0 8.0563 0 37.1831 0 27.3803 12.6197 50 slack 5 70 50 Ranging Flair Furniture Solution Value Reduced Original Val Lower Bound Upper Bound Variable 160 84 Dual Value SlackSurplus Original Val Lower Bound Upper Bound Infinity Infinity 40.8 600 1411429 Infinity 27.3803 37.1831 70 416667 50 21.875 Constraint Carpentry hours Painting hours Inspection hours Lumber (linear feet) Demand 18.9296 8.0563 240 221.0704 91,9437 19.5 63.3803 1.1972 0 36 1248 40 12.6197 27.3803