The Nosmell Nutrient Compnay 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 is sells to retailers around the country. Their ovjective 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): Nitrate = $280, Phosphate = 90, Potash = 179, and Inert ingredients = $20. Costs of mixing, packaging, and selling are identical for all three mizes and amount to $25 per ton. Prices for the fertilizer are (per ton): 5-10-5 = $80, 5-10-10 = 100, and 12-10-5 = $120. In addition, there is a sales commitment to deliver 400 tons of 5-10-5 from the current order.
a. Express this problem as an algebraic set of equations.
b. Set up and solbe the problem using Excel. You may use either Solver or QM.
c. What is the restrictive ingredient?
d. What is the impact if there is 10% more of this ingredient available?
e. Suppose that it costs 25% more for the additional quantity of this ingredient. How will that affect the optimal solution?
f. What are the management implications of using this technique?