NWAC Electronics manufactures four types of simple cables for a defense contract
ID: 3102661 • Letter: N
Question
NWAC Electronics manufactures four types of simple cables for a defense contractor. Each cable must go through four sequential operations: splicing, soldering, sleeving,and inspection. The contractor guarantees a minimum production level of 100 units for eachof the four cables. The following table provides pertinent data for the situation.
Minutes per unit
Cable Splicing Soldering Sleeving Inspection Unit Revenue ($)
1 10.5 20.4 3.2 5.0 9.40
2 9.3 24.6 2.5 5.0 10.80
3 11.6 17.7 3.6 5.0 8.70
4 8.2 26.5 5.5 5.0 7.80
Daily capacity 4800 9600 4700 4500
(a) (8 points) Formulate the problem as a linear programming model and determine the
optimal production schedule. You may use Excel Solver or AMPL.
(b) (8 points) Formulate the dual of this problem and solve.
(c) (4 points) Based on the dual prices, do you recommend making increases in the daily
capacities of any of the four operations? Explain.
Explanation / Answer
a) De nition of variables:
xi
is the number of units of cable i produced.
We write the problem as
maximize 9:4x1 + 10:8x2 + 8:75x3 + 7:8x4
subject to 10:5x1 + 9:3x2 + 11:60x3 + 8:2x4 4800
20:4x1 + 24:6x2 + 17:70x3 + 26:5x4 9600
3:2x1 + 2:5x2 + 3:60x3 + 5:5x4 4700
5:0x1 + 5:0x2 + 5:00x3 + 5:0x4 4500
x1 100
x2 100
x3 100
x4 100
The optimum solution is given by x1 = 100; x2 = 100; x3 = 138:418; x4 = 100, with optimal
objective function value 4011.1582.
b) The dual prices are y1 = 0; y2 = 0:49; y3 = 0; y4 = 0; y5 = 0:68; y6 = 1:36; y7 = 0; and
y8 = 5:30. Therefore, the only capacity (possibly) worth increasing is the soldering one.
c) It is a disadvantage. The negative values of y5; y6, and y8 tell us that decreasing the minimum
requirements for x1; x2, and x4 will increase the optimum objective function value.
d) A dual price tells us how much the optimal objective function value of the primal LP will vary
when we increase by one unit the RHS of the corresponding constraint. Therefore, we cannot
predict what will happen when the change is as large as 10%.
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