Stelle Office Supplies Inc. (SOSI) must fill an order for 2000 modular office dividers. Each divider consists of a frame, a set of legs, and a panel. SOSI has limited production and finishing time available and is considering the purchase of some of the components. Let x1, x2, and x3 be the number of frames, leg sets, and panels to make, and x4, x5, and x6 be the number of each to buy. The model reflects the costs to be minimized, the amount of production time, the amount of assembly time, and the need for 2000 of each component.
1) Specify the complete solution in terms of the decision variables, slacks/surpluses and the value of the objective function.
2) What will happen if SOSI management decided to buy 50 frames instead of manufacturing?
3) How much more expensive would legs have to be to manufacture before you would change your solution?
4) What would you be willing to pay for more production time?
5) What would happen if the amount of assembly time decreased by 2000 hours?
6) Explain clearly what you mean by dual price of -17.333 in respect of constraint number 4.
Min 20 x1+ 14 x2 + 15 x3 + 28 x4 + 20 x5 + 25 x6
s.t. 30 x1 + 40 x2 + 25 x3 ≤ 180000 (Production Hours)
15 x1 + 10 x2 + 30 x3 ≤ 90000 (Assembly Hours)
x1 + x4 = 2000
x2+ x5 = 2000
x3+ x6 = 2000
all xi ≥ 0
OPTIMAL SOLUTION:
Objective Function Value = 104666.667
Variable Value Reduced Costs
--------- -------- -------------------
Xl 2000.000 0.000
X2 2000.000 0.000
X3 1333.333 0.000
X4 0.000 3.000
X5 0.000 2.667
X6 666.667 0.000
Constraint Slack/Surplus Dual Prices
--------- -------- ----------------
1 6666.667 0.000
2 0.000 0.333
3 0.000 -25.000
4 0.000 -17.333
5 0.000 -25.000
OBJECTIVE COEFFICIENT RANGES:
Variable Lower Limit Current Value Upper Limit
------------ --------------- ----------------- ---------------
Xl -5.000 20.000 23.000
X2 -3.333 14.000 16.667
X3 9.000 15.000 25.000
X4 25.000 28.000 No Upper Limit
X5 17.333 20.000 No Upper Limit
X6 15.000 25.000 31.000
RIGHT HAND SIDE RANGES:
Constraint Lower Limit Current Value Upper Limit
--------------- --------------- ------------ ---------------
1 173333.333 180000.000 No Upper Limit
2 50000.000 90000.000 98000.000
3 666.667 2000.000 2380.952
4 0.000 2000.000 2210.526
5 1333.333 2000.000 No Upper Limit