Question

Hi I need some help with this.. can anyone explain?

A company blends nitrogen and phosphorous to produce two types of fertilizers. Fertilizer 1 must contain at least 50% nitrogen and sells for $55 per pound. Fertilizer 2 must contain at least 55% phosphorous and sells for $45 per pound. The company can purchase up to 9,000 pounds of nitrogen at $20 per pound and up to 15,000 pounds of phosphorous at $12 per pound. As the company’s Operations Manager, you are tasked to determine the optimal blend for both fertilizers and recommend the amount of nitrogen and phosphorous to purchase, bearing in mind that the company is a profit seeking company

In formulating this as a linear programming (LP) problem, let’s define the decision variables as follows:

N1 = amount of nitrogen (pound) used in Fertilizer 1

N2 = amount of nitrogen (pound) used in Fertilizer 2

P1 = amount of phosphorous (pound) used in Fertilizer 1

P2 = amount of phosphorous (pound) used in Fertilizer 2

 

The LP model is as shown: Let Z be the net profit = Revenue - Cost, MAX Z = $35N1 + $25N2 + $43P1 + $33P2

s.t.

N1 + N2 ≤ 9000 (Nitrogen Available)

P1 + P2 ≤ 15000 (Phosphorous Available)

0.5N1 – 0.5P1 ≥ 0 (Nitrogen Req for Fertilizer 1)

0.45P2 – 0.55N2 ≥ 0 (Phosphorous Req for Fertilizer 1)

N1, N2, P1, P2 ≥ 0

The Excel Solver solution outputs are as shown in Table 2-1 and Table 2-2.

(a) Interpret the Excel Solver solution and advise the management on the optimal blend for the fertilizers, the amount of nitrogen and phosphorous to purchase and the expected profit.

b) Suppose the company could acquire 1,000 pounds more of either nitrogen or phosphorous. Which should it choose? What would be the resulting impact on profit?

 

(c) Suppose the sales team update you that the selling price for Fertilizer 1 is $40 instead of $55. How would this change affect your decision?