Question

Appalachian Designs is a small manufacturer of furniture items that are sold throughout the summer at local festivals. Their production manager, J. P. Weaver, has to determine how many of each product to manufacture during the Spring production period. The products will require time on a planer, time on a lathe, and time in a finishing division. The time required for each product, the profit per unit, the maximum allowable production, the minimum production batch lot for each product, and the total hours available, are listed in the following table:

Products    Planer   Lathe     Finishing Profit Per Unit Maximum Production Min Batch Size

A                                .3         .05           .15                       $7.20                         700                        100*

B                                .2         .03           .08                       $5.80                        1000                      200

C                                .5         .12           .28                       $11.10                       300                         75

D                                .3         .07           .18                       $8.40                         600                        150

E                                 .4         .10           .22                       $9.30                         500                        100

      Hours Avail    300          80           200

*This means that for Product A, they may produce none at all, but if they produce, they must produce between 100 and 700 units. The same is true of all products.

Mr. Weaver would like to maximize profits, given the resources available. You are to provide the linear program that will assist him in these decisions.

Answer 1

Camlin Page Solution :- Linear programuning fookter: Let units be produced :- A di units B aa c x3 D du x5 101 Objecture > LPP: - Maximize : f= f = 7.22,+ 5.822 +110123 +8.4x4 + 9.3x5 15 Constraints :- :- subject ito :- 100 x < 700 200 sans 1oo 75 & dz<300 150 = du <600 100 = 15$ 500 or 21=0 12=0 23-0 du=0 x 5=0 20 0.381+ O222 +0.5X3 +0.3d4to-u26=300 0.0581+0.002+0.1288 to 0.0784 +0.1085=80 25) 0.1521+ 0 08%2+ 0.2879 +0.1804+0.2275= 200 30