2. (20 marks) A firm wishes to produce a single product at one or more locations so that the total monthly cost is minimized subject to demand being satisfied. At each location there is a fixed charge to be paid if any are produced (but is nil otherwise), and a variable cost which depends on whether the units are produced on regular time or on overtime. Each location has capacity restrictions on regular and overtime production. The relevant data are: Plant Fixed Regular Time Overtime Location Cost Unit Cost Capacity Unit Cost Capacity 1 2100 3.80 1200 4.60 500 2 1900 2.90 1500 4.10 600 3 2300 4.20 1800 5.60 800 4 1700 3.40 2000 4.20 550 5 2700 3.60 2900 5.10 650 6 2000 3.10 3000 4.90 900 Demand is for 8000 units per month. (a) Follow page 1 part (d). (b) Solve the model, and state the solution in words.