What are the constraints for this problem?
A production of 300 units of Twiddle Bugs, an educational toy for children, must be completed within 1 week by BugU Manufacturing. Two production lines are available, each for 30 hours during the week. Production line 1 can produce five units per hour and production line 2 can produce four units an hour. Line 1 costs $50 per hour to operate and line 2 costs $55 per hour. Overtime is available for line 1 at $15 per hour and for line 2 at $12 per hour. Management goals in decreasing order are:
P1: Produce 300 units.
P2: Maximum allowable overtime of 6 hours for line 1.
P3: Cost of overtime must not exceed $750.
P4: Avoid the underutilization of either production line. Assign weights that are proportional to their production capability.
P5: Producing more than 300 units is 1-1/2 times as undesirable as producing under 300 units.
Answer: Let x1 = hours of production time on line 1.
x2 = hours of production time on line 2.
5x1 + 4x2 = 300
x1≤ 30
x2 ≤ 30
P1: 5x1 + 4x2 + d1- - d1+ = 300
P2: x1 + d2- - d2+=36
P3: 50(x1 - 30) + 55(x2 - 30) + d2- - d2+ = 750 or 50x1 + 55x2 + d2- - d2+ = 3150
P4a: x1 + d4- - d4+=30
P4b: x2 + d5- - d5+=30
P5: See objective function.
Objective function: Minimize P1Ad1- + 1.5 P1Bd1+ + P2d2+ + P3d3+ + 5P4Ad4- + 4P4Bd5-
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