For the following linear program,

  Maximize            P= 5X_A+ 4X_B+12X_C

Subject to          18X_A+ 12X_B+6X_C ≤ 4800                 (Raw Material X)

                                9X_A+ 10X_B+2X_C ≤ 1800             (Direct Labor Hours)

                                2X_A+ 14X_B ≤ 2800 (Raw material Z)

Where                     X_A, X_B,X_C ≥ 0

The firm attempts to use linear programming to reach to the optimal mix of its products to maximize profit. The following is the Final simplex tableau; where three products are denoted by ( X_A,X_B, X_C) and the slack variables for resources Raw material X, Direct Labor Hours and Raw Material Z are denoted by ( S_X, S_L, S_Z respectively).

Basic mix 5 4 12 0 0 0

Xa Xb Xc Sx SL Sz Solution

12 Xc 3 2 1 1/6 0 0 800

0 SL 3 6 0 -1/3 1 0 200

0 Sz 2 14 0 0 0 1 2800

Sacrifice 36 24 12 2 0 0 9600

improvement -31 -20 0 -2 0 0

MCQ Questions

1.  The effect of increasing S_X by one unit is :

A. Decrease S_Lby ? hour

B. Increase X_Cby 1/6unit

C. No effect on S_Z

D. None of these

2.     If the raw material Z increased by one unit, then:

A. S_Z increased by one hour

B. X_A increased by half unit

C. No effect on X_C

D. None of these

3.     The effect of producing one unit from product A on the optimal solution is:

A.   X_Cincreased by 3units , S_L increased by 3hour and S_Z decreased by 2 units.

B.   X_C decreased by 3units , S_Ldecreased by 3hours and S_Z decreased by 2 units

C. There is no effect on the optimal solution

D. None of the above

pur-new-sol

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