The profit function for two products is Profit - -3x,2 +42x, - 3x2 + 46x2 + 700, where x, represents units of production of product 1 and x, 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 hours (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.) - 3x} +42x, - 3x3 + 46x, + 700 - 50T Max s.t 4x + 6x2 s 24 + OT *. *, OT 2 0 (b) Salve the optimization model you formulated in part (a). How much should be produced and how many overtime hours should be scheduled? What is the profit (in dollars)? (Round your answers to three decimal places.) Units of product 1 Units of product 2 Overtime hours *, - 3.666 X2 - 2.999 X X X OT = 8.666 Profit P= $887333