2. Three types of fertilizer are manufactured by a company - Regular, Supergro,
ID: 3152185 • Letter: 2
Question
2. Three types of fertilizer are manufactured by a company - Regular, Supergro, and Jungle Feeder. Regular should have at least 15 percent nitrogen and 16 percent phosphorous. Supergro should have at least 15 percent nitrogen and 18 percent phosphorous, and Jungle Feeder should have at least 16 percent nitrogen and 20 percent phosphorous. These are made by using two components – Component A and Component 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 1,500 pounds, while each of the others has a demand of 3,000 pounds.
Formulate the linear program for this situation to minimize total cost.
b) Minimize cost = 0.3R1 + 0.5R2 + 0.3S1 + 0.5S2 + 0.3J1 + 0.5J2
Subject to:
R1 + R2 = 1500 Total weight of regular
S1 + S2 = 3000 Total weight of Supergro
J1 + J2 = 3000 Total weight of Supergro
0.14R1 + 0.20R2 > 225 Note: 225 = 15%(1500)
0.18R1 + 0.24R2 > 240 Note: 240 = 16%(1500)
0.14S1 + 0.20S2 > 450 Note: 450 = 15%(3000)
0.18S1 + 0.24S2 > 540 Note: 540 = 18%(3000)
0.14J1 + 0.20J2 > 480 Note: 480 = 16%(3000)
0.18J1 + 0.24J2 > 600 Note: 600 = 20%(3000)
R1, R2, S1, S2, J1, J2 > 0
***********NEED HELP ON THIS PART*******************
For Regular Fertilizer
Total weight =
Cost per pound =
Pounds of Component A used =
% Nitrogen =
Pounds of Component B used =
% phosphorous =
For Supergro
Total weight =
Cost per pound =
Pounds of Component A used =
% Nitrogen =
Pounds of Component B used =
% phosphorous =
For Jungle Feeder
Total weight =
Cost per pound =
Pounds of Component A used =
% Nitrogen =
Pounds of Component B used =
% phosphorous =
For Regular Fertilizer
Total weight =
Cost per pound =
Pounds of Component A used =
% Nitrogen =
Pounds of Component B used =
% phosphorous =
For Supergro
Total weight =
Cost per pound =
Pounds of Component A used =
% Nitrogen =
Pounds of Component B used =
% phosphorous =
For Jungle Feeder
Total weight =
Cost per pound =
Pounds of Component A used =
% Nitrogen =
Pounds of Component B used =
% phosphorous =
Explanation / Answer
For 1000 lb of Regular is made up of A and B.
=> 1000 lb of Regular provides 100 lb N and 160 Lb P
100 = .14 A + .18 B
160 = .2 A + .24 B
or using all of A or all B until the 160 and 100 quantities are filled. You shoud use the cheapest combination. For Regular use 889 lb of A and 0 B gives 160 lb P and 124.4 lb N and cost $267
for Supergro use the cheap stuff exceeds 1000 lb so we must use some of the B to keep the total weight at 1000 lb. For cost effeciency we must use as little B as we need to.
2000 = (1-X)* 2222.22 + x* 1666.7
X = .4
Use 400 Lb A, 333.33 Lb B and total cost is $733.33
For Jungle..
2000 = (1-X)* 2222.22 + x* 1666.7
X = .22222
Use 1666.7 lbm of A, 333.3 lbm B and cost is $666.67.
2nd method-
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