question archive The P&T company needs to decide how many tons of frozen peas and carrots should be produced next week to earn the highest profit
The P&T company needs to decide how many tons of frozen peas and carrots should be produced next week to earn the highest profit
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The P&T company needs to decide how many tons of frozen peas and carrots should be produced next week to earn the highest profit. Market demand is random. A market investigation shows that the P&T company can sell at most 400 tons of frozen peas with proability 0.4 and 1000 tons with probability 0.6 next week, and sell at most 300 tons of frozen carrots with probability 0.7 and 800 tons with probability 0.3. The total maximum production rate of the P&T company is 1400 tons of frozen peas and carrots per week. The production costs of frozen peas and carrots are $1000 and $1500 per ton, respectively, and the selling prices are $2000 and $3000 per ton. The P&T company has to throw away the products which are not sold at the end of week. How many tons of frozen peas and carrots should the P&T company produce next week to maximize the expected net profit? Let x be the production quantity of frozen peas next week and y the production quantity of frozen carrots. Formulate a linear programming model for this prob- lem. Please use additional decision variables if needed and explain every constraint as clearly as you can.
