G and P Manufacturing would like to minimize the labor cost ofproducing dishwasher motors for major
appliance manufacturer. Two models of motors exist and the timein 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 ofArea 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 AreaC and a combined total of 4,000 hours are available to betransferred from Area A to Areas B and C.
We would like to develop the linear programming model tominimize the labor cost, whose solution would tell G&P how manyof 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 availabilityconstraint 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 alwayshave the highest resource availability.
- True
- False
- Let Pij = the production of product I in period j. To specifythat production of product 2 in period 4 and in period 5 differs byno 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.
