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THE TAIWAN ELECTRONIC COMMUNICATIONS (TEC) PROBLEM 131

Figure 3.19 Solution for the Digital Controls, Inc. Problem

Objective Function Value = 2170.000
Variable Value Reduced Costs
-------------- --------------- -----------------
AM 100.000 0.000
BM 60.000 0.000
AP 0.000 1.750
BP 90.000 0.000
Constraint Slack/Surplus Dual Prices
-------------- --------------- -----------------
1 0.000 –12.250
2 0.000 –9.000
3 20.000 0.000
4 0.000 0.375

OBJECTIVE COEFFICIENT RANGES
Variable Lower Limit Current Value Upper Limit
------------ --------------- --------------- ---------------
AM No Lower Limit 10.000 11.750
BM 3.667 6.000 9.000
AP 12.250 14.000 No Upper Limit
BP 6.000 9.000 11.333
RIGHT HAND SIDE RANGES

Constraint Lower Limit Current Value Upper Limit
------------ --------------- --------------- ---------------
1 0.000 100.000 111.429
2 60.000 150.000 No Upper Limit
3 580.000 600.000 No Upper Limit
4 600.000 1080.000 1133.333

c. Suppose that the manufacturing cost increases to E11.20 per case for model A and the
manufacturing cost for model B decreases to E5 per unit. Would the optimal solution
change? Use the 100 per cent rule and discuss.

17 Tucker Inc. produces high-quality suits and sport coats for men. Each suit requires 1.2 hours
of cutting time and 0.7 hours of sewing time, uses six metres of material, and provides a profit
contribution of E190. Each sport coat requires 0.8 hours of cutting time and 0.6 hours of
sewing time, uses four metres of material, and provides a profit contribution of E150. For the
coming week, 200 hours of cutting time, 180 hours of sewing time and 1200 metres of fabric
are available. Additional cutting and sewing time can be obtained by scheduling overtime for
these operations. Each hour of overtime for the cutting operation increases the hourly cost by
E15, and each hour of overtime for the sewing operation increases the hourly cost by E10. A
maximum of 100 hours of overtime can be scheduled. Marketing requirements specify a
minimum production of 100 suits and 75 sport coats.
S ¼ number of suits produced

SC ¼ number of sport coats produced
D 1 ¼ hours of overtime for the cutting operation
D 2 ¼ hours of overtime for the sewing operation

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