Problem No. 4 A production plan for 12 months and one products needs to be optimized for maximum profit. The product requires 1.5 hours to assemble. The monthly available demand is given below. The unit cost of the product is $25.50 in addition to the assembly labor. While each worker is available for 160 hours each month, only the time they spend on these products need to be accounted for in the cost. Shortages, at a cost of $20 per unit are allowed but all demand must be met by the end of the year. Monthly inventory carrying charge is $1.05 per unit. Hourly wages are $27.50, including benefits. There is hiring or firing ($ 4000 and $7000 each, respectively) and the available labor force is 20 workers. No overtime. The selling price is $199.99. No initial inventory and there should be no inventory at the end of period 12. Write all the necessary equations. Problem No. 4 A production plan for 12 months and one products needs to be optimized for maximum profit. The product requires 1.5 hours to assemble. The monthly available demand is given below. The unit cost of the product is $25.50 in addition to the assembly labor. While each worker is available for 160 hours each month, only the time they spend on these products need to be accounted for in the cost. Shortages, at a cost of $20 per unit are allowed but all demand must be met by the end of the year. Monthly inventory carrying charge is $1.05 per unit. Hourly wages are $27.50, including benefits. There is hiring or firing ($ 4000 and $7000 each, respectively) and the available labor force is 20 workers. No overtime. The selling price is $199.99. No initial inventory and there should be no inventory at the end of period 12. Write all the necessary equations