# Quain Case Analysis Essay examples

1005 Words Mar 26th, 2015 5 Pages
Cory Maillet
Krisandra Horn

Quain Lawn and Garden, Inc. Case Analysis

After a false retirement Bill and Jeanne Quain realized their destined action in the plant and shrub business. The need for a high-quality commercial fertilizer prompted the innovation of a blended fertilizer called “Quain-Grow”. Working with chemists at Rutgers University, a mixture was constructed from four compounds, C-30, C-92, D-21 and E-11. The costs for these four compounds per pound is as follows:
CHEMICAL COMPOUND
COST PER POUND
C-30
\$0.12
C-92
\$0.09
D-21
\$0.11
E-11
\$0.04

Specifications (i.e constraints) for the mixture demanded that Chemical E-11 must constitute for at least 15% of the blend, C-92 and C-30 must together constitute at least 45% of the
The first shows the impact of changing the objective function coefficients on the optimal solution and gives the range of values (lower and upper bound) for which the optimal solution remains unchanged. The second part of the report shows the impact of changing the R.H.S of the constraints of the objective function value, with the help of Dual Value (Shadow Price), with the lower and upper bounds for which the shadow price is valid. The results of this analysis in POM are as follows:

Variable
Value
Reduced Cost
Original Val
Lower Bound
Upper Bound

7.5
0
.12
.09

15
0
.09

.12

0
.1
.11
.01

27.5
0
.04

.12

Constraint
Dual Value
Slack/Surplus
Original Val
Lower Bound
Upper Bound
Constraint 1
0
20
7.5

Constraint 2
- .08
0
22.5
15
42.5
Constraint 3
.03
0
15
0

Constraint 4
- .04
0
50
30

Lastly, these results explain that the price of C-30 can vary within the range of .09 to Infinity without affecting the optimal solution. Likewise the range for C-92 is between –Infinity and .12, the range for D-21 is between 15 and 42.5, and the range for E-11 is between 30 and Infinity. The second part of this sensitivity analysis show the ranges for which the shadow prices are valid. Constraint 1 has a dual value of 0 and is valid between –Infinity and 27.5. Constraint 2 has a dual value of -.08 and is valid between 15 and 42.5. Constraint 3 has a dual value of .03 and is valid between 0 and 22.5. Finally, Constraint 4 has a dual