MM Inc, a manufacturing company, faces the forecasted demand shown in the table below. Cost of regular production is $8 per unit, the cost of subcontracting is $22 per unit, and the cost of carrying a unit in inventory from one month to the next is $4. Due to an agreement with a union, any employee that works at this plant receives an hourly wage of $12 and those employees that work overtime receive 50% premium. The cost of backordered item is $15. A regular work shift is 9 hours and there are 20 working days per month. On January 1", MM Inc has 2500 units of inventory and 65 employees. MM Inc can change the size of their work force. The cost of hiring and training a regular worker is $1800. Every laid off worker receives an equivalent of one monthly wage based on regular working hours only. Month Jan Feb Demand 31,100 45,750 63,540 79,800 102,200 65,400 March April May June I The labor contract at the plant prohibits overtime to exceed 3 hours per employee per day and subcontracting output to exceed 5000 units in any month. Each worker requires 12 minutes to produce one unit. If workers work overtime hours, their productivity drops by 20% due to fatigue. MM Inc's warehouse facility can only accommodate up to 15000 of inventory. To protect their brand, MM Inc does not allow for more than 2000 units to back ordered at any given month. produce one unit. If workers work overtime hours, their productivity drops by 20% due to fatigue. MM Inc's warehouse facility can only accommodate up to 15000 of inventory. To protect their brand, MM Inc does not allow for more than 2000 units to back ordered at any given month. a) Formulate aggregate planning LP and provide an estimate for overall supply chain costs