G and P Manufacturing would like to minimize thelabor cost of producing dishwash

Question

G and P Manufacturing would like to minimize thelabor 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 raw material cost. Model 1 Model 2 Area A (hrs) 25 Area B (hrs) Area C (hrs) Cost (S) 100 Currently, labor assignments provide for 25,000 hours in Area A, 36,000 hours in Area B and 24,000 hours in area C. 2,000 hours are available to be transferred from Area C to Area A and a combined total of 4,000 hours are available to be transferred from Area B to Areas Aand 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. P1 the number of model 1 motors to produce Let P2 the number of model 2 motors to produce TCA the number of hours transferred from C to A TBA m the number of hours transferred from B to A

Explanation / Answer

Below represents the resource availability constraint of for Area A

25P1 + 18P2 <= 25000 + TCA + TBA

Here, 25P1 is the time taken by Model 1 in area A and 18P2 is the time taken by Model 2 in area A.
25000 is the total available time in area A. Extra TCA and TBA is available to be transferred from C and B to A.

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