Problem:

The Nosmell Nutrient Company has placed an order for the coming month for 500 tons of nitrate, 800 tons of phosphate, and 1,200 tons of potash. The company blends these ingredients together with certain inert ingredients (that are available in unlimited supply) to make three popular fertilizer mixes that it sells to retailers around the country. Their objective is to maximize profits in the coming month.

The three basic fertilizers are 5-10-5, 5-10-10, and 12-10-5, the numbers representing the percentage (by weight) of nitrate, phosphate, and potash in each of the mixes. The remainder of the mixture is made up of the inert material that is available in unlimited supply.

The cost of the fertilizer is (per ton)

Costs of mixing, packaging, and selling are identical for all three mixes and amount to $25 per ton.

Prices for the fertilizer are (per ton)

In addition, there is a sales commitment to deliver 400 tons of 5-10-5 from the current order.

Required:

Question 1: What are the decision variables in this problem?

Question 2: What are the constraint variables in this problem?

Question 3: What technique is best suited for determining the optimum solution? Support your decision.

Question 4: Express this problem as an algebraic set of equations as shown in the text.

Question 5: Solve the problem using either Solver, QM or by hand calculation. Show all your work.

Question 6: What is the restrictive variable? Support your answer.

Note: Please provide equation and explain comprehensively and give step by step solution.