Stelle Office Supplies (SOS) must fill an order for 2000 modular office dividers. Each divider consists of a frame, a set of legs, and a panel. SOS 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, respectively, and let x4, x5, and x6 be the number of each to buy, respectively. 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.
a. Calculate the range of optimality for all of the objective function coefficients.
b. Calculate the range of feasibility for the first two right-hand sides.
c. How much less expensive would it have to be to buy frames before you would consider it?
d. How much more expensive would legs have to be to make before you would change your solution?
e. What would the total cost be if the cost to make a panel increased by $3.00?
f. What would you be willing to pay for more production time?
g. What would happen to the total cost if the amount of assembly time decreased by 2000 hours?
a. ?? < c1 ? 23
?? < c2 ? 16.67
9 ? c3 ? 25
25 ? c4 < ?
17.33 ? c5 < ?
15 ? c6 ? 31
b. 173,333.33 ? b1 < ?
50,000 ? b2 ? 98,000
6666.67 ? b3 ? 2380.95
0 ? b4 ? 2210.53
1333.33 ? b5 < ?
c. $3.00 per frame
d. $2.67 additional
e. Cost would increase by 1333.33(3) = 4000.
f. nothing
g. 0.33(2000) = 666.67 more cost
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