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1) The profit function for two products is
Profit = -7X2+38X-3Y2+45Y+790
Where X represents units of production of product X and Y represents units of production of product Y. Producing one unit of product X requires 5 labor-hours and producing one unit of product Y requires 10 labor-hours. Currently, 50 labor-hours are available. The cost of labor-hours is already factored into the profit function.
a) Formulate a mathematical model that can be used to determine the optimal production quantity of products X and Y. The quantity produced should be integers.
b) Solve the optimization model you formulated in part (a). How much should be produced and what is the optimal profit?
X=
Y= Optimal profit= $
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