Question

1. Three types of fertilizer are manufactured by a company: Regular, Supergro, and Jungle Feeder. Regular should have at least 10 percent nitrogen and 16 percent phosphorous. Supergro should have at least 12 percent nitrogen and 20 percent phosphorous, and Jungle Feeder should have at least 15 percent nitrogen and 18 percent phosphorous. These are made by using two components: A and B. Component A costs $0.30 per pound and is 14 percent nitrogen and 18 percent phosphorous. Component B costs $0.50 per pound and is 20 percent nitrogen and 24 percent phosphorous. The demand for Regular is projected to be 500 pounds, while each of the others has a demand of 1000 pounds.

Let x1 = lbs of A in Regular, x2= lbs of A in Supergro, x3= lbs of A in Jungle Feeder,

      x4= lbs of B in regular, x5=lbs of B in Supergro, x6=lbs of B in Jungle Feeder

Min. Z = .3X1 + .3X2 + .3X3 + .5X4 + .5X5 + .5X6

S.T.

x1+ x4 = 500

x2 + x5= 1000

x3 + x6 = 1000

0.14x1 + 0.20x4 ≥ 100

0.18x1 + 0.24x4 ≥ 160

0.14x2 + 0.20x5 ≥ 240

0.18x2 + 0.24x5 ≥ 400

0.14x3 + 0.20x6 ≥ 300

0.18x3 + 0.24x6 ≥ 360

For all xi ≥ 0

Upload your spreadsheet with the answer on sheet 2

How many pounds of each component will they need and how much will it cost?

Answer 1

Your first 3 constraints are correct, but the last six are incorrect. The last six should be as follows:

0.14x1 + 0.20x4 ≥ 0.10(x1 + x4), that is 0.04x1 + 0.1x4 ≥ 0

0.18x1 + 0.24x4 ≥ 0.16(x1 + x4), that is 0.02x1 + 0.08x2 ≥ 0

0.14x2 + 0.20x5 ≥ 0.12(x2 + x5), that is 0.02x1 + 0.08x5 ≥ 0

0.18x2 + 0.24x5 ≥ 0.2(x2 + x5), that is -0.02x2 + 0.04x5 ≥ 0

0.14x3 + 0.20x6 ≥ 0.15(x3 + x6), that is -0.01x3 + 0.05x6 ≥ 0

0.18x3 + 0.24x6 ≥ 0.18(x3 + x6), that is 0.06x6 ≥ 0

The optimal solution is shown in the Results area.

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