Question

A wood products firm uses leftover time at the end of each week to make goods for stock. Currently, there are 2 products on the list of items that are produced for stock: a chopping board and a knife holder. Both items require three operations: cutting, gluing, and finishing. The manager of the firm has collected the following data on these products:

Chopping board Profit per unit: $2 Cutting: 1.4

Gluing: 5 Finishing: 12

Knife holder: Profit per unit: $6 Cutting: .8 Gluing: 13 Finishing:3

The manager has also determined that during each week 56 minutes are available for cutting, 650 minutes are available for gluing and 360 minutes are available for finishing.

A. Formulate this problem as a linear programming model.

B. Determine the optimal quantities of the decision variables.

C. Which resources are not completely used by your solution? How much of each resource is unused?

Answer 1

Date Product Time Required in munites Recapit lutting Cliopping board knife holder 2 6 13 650 3 360 Time Captivailability 56 items i, e g Chopping the ferm. Haximise Chopat) 5 Let xi andres lee the no. muits board and linden produced by z = 2x1 t6u2 subjed to constraints 1.401 10 8 12 <56 5 nit 13 uz < 650 lQuit 3 u2 < 360 41, 4270. Jultraducesy okade kassalelos, Sandoz to comment the custo- -auit unequalities into equations, Maxinize z= Quitbud tosi tos tos3 Mubied to constraints 1.UNI HOB n 2 t si = 56 8x1 + 1342 + s = 656 1201 + 3 x 2 + 83=360 XI H2, S1, S2, S3 20 u en initial leasie feonible solution is? UFO, ke=0 s1=56 S2 = 650, 33=360 +

surplen Zalele 2 G Basic Solution W 23 Ss S2 S3 Ratio Varialele Suplex Falele 2 solution 6 22 o Si 0 0 S2 S3 OUI Ratio it Basic Variabele 1.4 O S) S S3 0 O 56 658 360 0.8 13 5 12 0 70 Joe 120 3 O O potoo O O O O i 0 O اکی 16 71/65 6. 22 S3 SO 210 300 5/13 191/13 30/13 -4/13 0 6 O oooo 81,30 0 V13 O -3113 1 6/13 0 -6113 o G uits og G-2 sunce, all the enteries in the ori nw arezerwa Angature , optinium latest has been obtained. Leoritis Maximum when the finis puoduces Sounits Tie, kruiife holder ando units huice, Chopping board, Maximum perosit The forest and third fiesblouse is not completely utilied. Oletning Ciluing 216 thatg finishing is 210 = 30 and that