Three types of fertilizer are manufactured by a company _____ Regular, Supergro,

Question

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 tow component _____ 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. Using the variables defined below to formulate the appropriate objective function and constraints. Let X_1 = pounds of component A in 1000 pounds of Regular X_2 = pounds of component A in 2000 pounds of Supergro X_3 = pounds of component A in 2000 pounds of Jungle Feeder X_4 = pounds of component B in 1000 pounds of Regular X_5 = pounds of component B in 2000 pounds of Supergro X_6 = pounds of component B in 2000 pounds of Jungle Feeder

Explanation / Answer

Solution:

The computation are expressed below,

Nitrogen Phosphorous

Regular 10 % 16%

Supergro 12% 20%

Jungle 15% 18%

A($0.30/lb) 14% 18%

B($0.50/lb) 20% 24%

Regular = X1 = 1000 lb --> 100 lb N and 160 lb P = Component A --> $0.30*850=$255

Supergro = X2 = 2000 lb --> 240 lb N and 400 lb P = Component A --> $0.30*1600 = $480

Jungle feeder = X3 = 2000 lb --> 300 lb N and 360 lb P = Component A --> $0.30*1700 = $510

Regular = X4 = 1000 lb --> 100 lb N and 160 lb P = Component B --> $0.50*850=$425

Supergro = X5 = 2000 lb --> 240 lb N and 400 lb P = Component B --> $0.50*1600 = $800

Jungle feeder = X6 = 2000 lb --> 300 lb N and 360 lb P = Component B --> $0.50*1700 = $850

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