G and P Manufacturing would like to minimize the labor cost of producing dishwasher motors for major
appliance manufacturer. Two models of motors exist and the time in hours required for each model in each
production area is tabled here, along with the labor cost.
Model 1
Model 2
Area A (hrs)
12
16
Area B (hrs)
10
8
Area C (hrs)
14
12
Cost ($)
100
120
Currently, labor assignments provide for 38,000 hours in each of Area A, 25,000 hours in Area B, and 27,000 hours in area C.
2,000 hours are available to be transferred from Area B to Area C and a combined total of 4,000 hours are available to be transferred from Area A to Areas B and C.
We would like to develop the linear programming model to minimize the labor cost, whose solution would tell G&P how many of each model to produce and how to allocate the workforce.
Let P1 = the number of model 1 motors to produce
P2 = the number of model 2 motors to produce
TAC = the number of hours transferred from A to C
TAB = the number of hours transferred from A to B
TBC = the number of hours transferred from B to C
What is the objective function?
Max 14 P1 + 12 P2
Min 10 P1 + 8 P2
Min 100 P1 + 120 P2
Max 100 P1 + 120 P2
Min 12 P1 + 16 P2
Which of the following represents the resource availability constraint for Area B?
10P1 +8P2 <= 25,000
10P1 +8P2 <= 25,000 -TBC + TBA
10P1 +8P2 <= 25,000 +TBC – TAB
10P1 +8P2 <= 25,000 -TBC + TAB
10P1 +8P2 <= 25,000 – 2,000 + 4,000
No matter what the resource allocation is, Area A will always have the highest resource availability.
True
False
Let Pij = the production of product I in period j. To specify that production of product 2 in period 4 and in period 5 differs by no more than 80 units, we need to add which pair of constraints?
P24 – P25 >= 80; P25 – P24 >= 80
P24 – P25 <= 80; P25 – P24 <= 80
P24 – P25 <= 80; P25 – P24 >=80
P52 – P42 <= 80; P42 - P52 <= 80
None of the other above.