1. The manufacturing department of the Thomas Lee Company is planning its production level over the next six months. Based on orders received and sales forecasts provided by the marketing department, the estimate of monthly demand forecast for the twelve-month period is as follows: The monthly unit holding cost is $4, the cost of hiring a worker is $3000; the cost of laying off a worker is $2000. Regular employee works 40 hours per week with monthly salary of $3200 and the cost of utilizing overtime is 1.5 times the regular time labor cost. Each worker can produce 50 units per month during regular time and each worker can work no more than 10 hours of overtime per week. Current starting inventory is 500 units, the initial workforce level is 150 and the maximum physical production capacity is 20000 units per month. We may assume that there are 4 weeks in a month. Thomas Lee would like to find the optimal (i.e., least cost) production plan. (a) (15 points) Formulate a linear program to solve this problem. Define your decision variables and explain the constraints. (b) (15 points) Solve the linear program