a) Write the algebraic model for this problem

b) Solve the model using LINGO

c) State the solution in words.

2. (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 @ $2.70/kg. Next 6000 Tonnes (or any fraction) may be purchased @ $3.70/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 $1.50 5500 2 $1,200,000 $2.20 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 $5.10 per kg. They wish to know what they should do to maximize their annual profit