G and P Manufacturing would like to minimize the labor cost of producing dishwas

Question

G and P Manufacturing would like to minimize the labor cost of producing dishwasher motors for a major appliance manufacturer. Although two models of motors exist, the finished models are indistinguishable from one another; their cost difference is due to a different production sequence. The time in hours required for each model in each production area is tabled here, along with the labor cost. Area A Area B Area C Cost Model I 15 4 4 80 Model 2 10 65 Currently labor assignments provide for 10,000 hours in each of Areas A and B and 18000 hours in Area C. If 2000 hours are available to be transferred from area B to Area A, 3000 hours are available to be transferred from area C to either Areas A or B, develop the linear programming model whose solution would tell G&P; how many of each model to produce and how to allocate the workforce.

Explanation / Answer

Let,

X1 = Number of Model 1 produced
X2 = Number of Model 2 produced
T1 = Hours transferred from B to A
T2 = Hours transferred from C to A
T3 = Hours transferred from C to B

Objective Function: Minimize. Z = 80X1 + 65X2

Subject to,

15X1 + 3X2 10000 + T1 + T2 (Resultant available hours in A)
4X1 + 10X2 10000 - T1 + T3 (Resultant available hours in B)
4X1 + 8X2 18000 - T2 - T3 (Resultant available hours in C)

T1 2000
T2 + T3 3000

X1, X2, X3, T1, T2, T3 0

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Note: The above model, if implemented, however, will always give X1=X2=0 because there is no '' constraint as per the problem. So, instead of having a minimum cost model, a maximum profit model should be used after knowing the selling price of the models.

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