Three types of fertilizer are manufactured by a company epsilon Regular, Supergr

Question

Three types of fertilizer are manufactured by a company epsilon Regular, Supergro, and Jungle Feeder. Regular should have no more than 10 percent nitrogen and 16 percent phosphorous. Supergro should have no more than 12 percent nitrogen and 20 percent phosphorous, and Jungle Feeder should have no more than 15 percent nitrogen and 18 percent phosphorous. These are made by using two components epsilon 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 1,000 pounds, while each of the others has a demand of 2,000 pounds. Formulate the appropriate linear program, solve using the QM and interpret the results. Let X1 = pounds of component A in Regular X2 = pounds of component A in Supergro X3 = pounds of component A in Jungle Feeder X4 = pounds of component B in Regular X5 = pounds of component B in Supergro X6 = pounds of component B in Jungle Feeder

Explanation / Answer

As given in question, Let
X1 = pounds of component A in Regular
X2 = pounds of component A in Superagro
X3 = pounds of component A in Jungle Feeder
X4 = pounds of component B in Regular
X5 = pounds of component B in Superagro
X6 = pounds of component B in Jungle Feeder

We need to minimize this :

Hence general formula :
Nitrogen % = (Amt. of A)*14/1000 + (Amt. of B)*20/1000
Phosphorus % = (Amt. of A)*18/1000 + (Amt. of B)*24/1000

Hence, constraints will be :

Solving these we will get, (rounding off to nearest integer)

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