2. Jim Jones manufactures inexpensive set-it-yourself furniture for college stud

Question

2. Jim Jones manufactures inexpensive set-it-yourself furniture for college students. He currently makes two products: bookcases and tables. Each book case contributes $6 to profit, and each table contributes $5 to profits.

Each product passes through two processes: cutting and finishing. A bookcase takes 4 hours of cutting and 4 hours of finishing. A table requires 3 hours of cutting and 5 hours of finishing. There are currently 400 hours of cutting available and 300 hours of finishing available. Jim Jones objective is to maximize profits.

                      CUTTING            FINISHING        Profit/Unit

Bookcase           4 hrs                 4 hrs                 $6

Table                 3 hrs                 5 hrs                 $5

Available

Capacity/week     400 hrs               300 hrs

Clearly state your decision variables and formulate Jim Jones’ problem as a linear program that maximizes Jim Jones’ weekly profit.

Explanation / Answer

Entering =X1=X1, Departing =S2=S2, Key Element = 44

R2R2 (new) =R2=R2 (old) ÷4=R2÷4=R2 (old) 1414

R1R1 (new) =R1=R1 (old) 4R2-4R2 (new)

Since all CjZj0Cj-Zj0,

Optimum Solution is arrived with value of variables as :
X1=75

X2=0

Maximise Z=450

MAX Z= 6 X1+ 5 X2 Subject to constraints 4 X1+ 3 X2 400 44 X1+X1+ 55 X2X2 300300 and X1,X20X1,X20

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