Solution for QID #34568: For the following linear program, MaximizeP= 5XA+ 4XB+12X | StudyHelpMe

For the following linear program,    Maximize            P= 5XA+ 4XB+12XC   Subject to          18XA+ 12XB+6XC ≤ 4800                 (Raw Material X)                                 9XA+ 10XB+2XC ≤ 1800             (Direct Labor Hours)                                 2XA + 14XB             ≤ 2800 (Raw material Z)  Where                     XA, XB,XC  ≥ 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 ( XA,XB, XC) and the slack variables for resources Raw material X, Direct Labor Hours and Raw Material Z are denoted by ( SX, SL, SZ 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 SX by one unit is : A. Decrease SL by ? hour            B. Increase XC by 1/6unit C. No effect on SZ                                                                   D. None of these   2.     If the raw material Z increased by one unit, then: A. SZ increased by one hour        B. XA increased by half unit C. No effect on XC                                                                  D. None of these   3.     The effect of producing one unit from product A on the optimal solution is:       A.   XC  increased by 3units , SL increased by 3hour and SZ decreased by 2 units. B.   XC  decreased by 3units , SL decreased by 3hours and SZ decreased by 2 units    C. There is no effect on the optimal solution D. None of the above