Question: The profit function for two products is Profit = -3x,? + 42x4 - 3x2? + 46x2 + 700, where x, represents units of production of

The profit function for two products is Profit =

The profit function for two products is Profit = -3x,? + 42x4 - 3x2? + 46x2 + 700, where x, represents units of production of product 1 and xz represents units of production of product 2. Producing one unit of product 1 requires 4 labor-hours and producing one unit of product 2 requires 6 labor-hours. Currently, 24 labor-hours are available. The cost of labor-hours is already factored into the profit function. However, it is possible to schedule overtime at a premium of $5 per hour. (a) Formulate an optimization problem that can be used to find the optimal production quantity of product 1 and the optimal number of overtime hours to schedule. (Let OT be the number of overtime hours scheduled.) Max s.t.

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