G and P Manufacturing would like to minimize the labor cost of producing dishwasher motors for a 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 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 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

T_AC = the number of hours transferred from A to C

T_AB = the number of hours transferred from A to B

T_BC = the number of hours transferred from B to C

1. What is the objective function?

Max 14 P1 + 12 P2

Min 12 P1 + 16 P2

Max 100 P1 + 120 P2

Min 100 P1 + 120 P2

Min 10 P1 + 8 P2

2. Which of the following represents the resource availability constraint for Area B?

10P1 + 8P2 <= 25,000 TBC + TAB

10P1 + 8P2 <= 25,000

10P1 + 8P2 <= 25,000 2,000 + 4,000

10P1 + 8P2 <= 25,000 - TBC + TBA

10P1 + 8P2 <= 25,000 + TBC - TAB

3. No matter what the resource allocation is, Area A will always have the highest resource availability.

True

False