3. (20 marks) A company buys fresh fish for processing. They have an annual contract with their supplier to buy up to 10,000 Tonnes at the following set of incremental prices: First 4000 Tonnes (or any fraction) may be purchased @ $2.80/kg. Next 6000 Tonnes (or any fraction) may be purchased @ $3.80/kg. Their fish processing plant can operate on a one or two shift per day basis. (Shift two operates only if shift one operates.) For each shift there is a fixed cost which exists if the shift operates, but is nil otherwise, and a variable cost per kilogram of fish processed. The costs and shift capacities are: Fixed Cost Variable Cost Annual Capacity Per Annum Per Kilogram (Tonnes) 1 $1,800,000 $1.60 5500 2 $1,200,000 $2.30 6000

If a shift operates at all, then the minimum amount processed is 2500 Tonnes per annum on that shift (i.e. the amount processed on any shift is either 0 or greater than or equal to 2500 Tonnes). The company sells processed fish for $5.00 per kg. They wish to know what they should do to maximize their annual profit. (a) Write the algebraic model for this problem. (b) Solve the model using LINGO or the Excel Solver. (c) State the solution in words.