G and P Manufacturing Would Like to Minimize the Labor

Essay

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. $$\begin{array} { c | c c } & \text { Model 1 } & \text { Model 2 } \\\hline \text { Area } A & 15 & 3 \\\text { Area B } & 4 & 10 \\\text { Area C } & 4 & 8 \\\hline \text { Cost } & 80 & 65\end{array}$$ 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.