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linear programming problem! help!?
original objective function: max 10S+9D
constraints:
cutting and dyeing: 7/10S+1D <=630
sewing: 1/2S+5/6D <=600
finishing 1S+2/3D <=708
inspection & packaging 1/10S+1/4D <=135
S, D >= 0
Suppose that Par, Inc., management encounters the following situations:
a. The accounting department revises its estimate of the profit contribution for the deluxe bag to $18 per bag.
b. A new low-cost material is available for the standard bag, and the profit contribution per standard bag can be increased to $20 per bag. (Assume that the profit contribution of the deluxe bag is the original $9 value.)
c. New sewing equipment is available that would increase the sewing operation capacity to 750 hours. (Assume that 10A +9B is the appropriate objective function.)
If each of these situations is encountered separately, what is the optimal solution and the total profit contribution?
1 Answer
- SqdancefanLv 73 years ago
Often, these problems are best solved graphically if there are only a couple of variables. See the source link.
initial problem: maximize 10S +9D
.. (S, D) = (540, 252)
.. total profit = 7668
a) maximize 10S +18D
.. (S, D) = (300, 420)
.. total profit = 10560
b) maximize 20S +9D
.. (S, D) = (708, 0)
.. total profit = 14160
c) maximize 10S +9D
.. (S, D) = (540, 252)
.. total profit = 7668
The capacity of the sewing operation is not a constraint at any point. Increasing that capacity has no value. (The area related to sewing capacity is shown as blue on the graph. The other operations constrain output to values below either limit imposed by the blue lines.)
Source(s): https://www.desmos.com/calculator/cq7fohbzqr
