TC Corp, a manufacturing company, faces the forecasted demand shown in the table below. Cost of regular production is $7 per unit, the cost of subcontracting is $25 per unit, and the cost of carrying a unit in inventory from one month to the next is $2. Due to an agreement with a union, any employee that works at this plant receives an hourly wage of $8 and those employees that work overtime receive 50% premium. The cost of backordered item is $20. A regular work shift is 10 hours and there are 22 working days per month. On January 1", TC Corp has 3000 units of inventory and 70 employees. TC Corp can change the size of their work force. The cost of hiring and training a regular worker is $1300. Every laid off worker receives an equivalent of one monthly wage based on regular working hours only. Month Jan Feb March April May June Demand 33,000 42,000 62,000 74,000 118,000 59,000 The labor contract at the plant prohibits overtime to exceed 2 hours per employee per day and subcontracting output to exceed 5000 units in any month. Each worker requires 20 minutes to produce one unit. If workers work overtime hours, their productivity drops by 33% due to fatigue. TC Corp's warehouse facility can only accommodate up to 15000 of inventory. To protect their brand, TC Corp does not allow for more than 1000 units to back ordered at any given month. a) Formulate aggregate planning LP and provide an estimate for overall supply chain costs. b) TC Corp is considering creating a promotion either during its off-peak month of January or peak month of May. The regular price for their product is $20 and their marketing department projects that a 20% discount will generate additional 25% growth in a demand. The marketing department also suspects that a discount will lead to the forward buying of 35% of the subsequent month's demand. c) Reconsider part a of the problem if TC Corp can hire temporary workers and then lay them off at any time. The cost of hiring and training a temporary worker is $200. Hired temporary workers work along with full-time employees during regular working hours and receive the same wage. Due to a lack of experience and a brief training procedure, temporary workers require 40 minutes to produce one unit during the first month of their employment. After the first month of their employment the temporary workers can cut their production time by 25%. Re-formulate aggregate planning LP solve it in Excel, and advice whether TC Corp should employ temporary workers. In your response: Provide a problem formulation for parts (a) and (c) (advice: you can do it in an MS Word document) Solution for each part in Excel (advice: you can separate spreadsheet for each scenario in a single Excel file)