A contractor forecasts the following demand for precast concrete elements for each of the next six month: Month 1 2 3 4 5 6 Demand 5,000 6,000 5,000 9,000 6,000 5,000 It takes a worker 15 minutes to produce one precast concrete element. Each worker works 150 hours per month plus up to 40 hours per month of overtime. A worker is paid a regular salary of $2,000 per month plus $50 per hour for overtime. At the beginning of each month, the contractor can either hire or fire workers. It costs the company $1,500 to hire a worker and $1,900 to fire a worker. The monthly holding cost per precast concrete item is 3% of the cost of producing an item with regular-time labor. (The raw materials in a precast concrete item is $10.) Formulate an LP that minimizes the cost of meeting (on time) the demands of the next six months. At the beginning of month 1, the contractor has 13 workers. Solve the LP using CPLEX. (fractional number of workers is acceptable)