Quain Case Analysis
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 blend, and D-21 and C-92 can together constitute no more than 30% of the blend. Lastly, Quain-Grow is packaged and sold in 50-pound bags. The objective of this analysis is to determine what blend of the four chemicals will allow Quain to minimize the cost of a 50-lb bag of the fertilizer. To do this we have used Linear Programming (LP) – a technique specifically designed to help managers make decisions relative to the allocation of resources. In this case, C-30 = , C-92 = , D-21 = , and E-11 = . The constraints for this case were translated into linear equations (i.e. inequalities) to mathematically express their meaning. The first constraint that C-11 must constitute for at least 15% of the blend can be expressed as: . The second constraint that C-92 and C-30 must together constitute at least 45% of the blend can be expressed as: . The third constraint that D-21 and C-92 can together constitute no more than 30% of the blend can be expressed as: . Lastly, the fourth constraint is that Quain-Grow is packaged and sold in 50-lb bags can be expressed as: . These equations were obtained and entered into a POM LP as a minimizing function. The objective function of this case was calculated and expressed as . The following table is the input
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 blend, and D-21 and C-92 can together constitute no more than 30% of the blend. Lastly, Quain-Grow is packaged and sold in 50-pound bags. The objective of this analysis is to determine what blend of the four chemicals will allow Quain to minimize the cost of a 50-lb bag of the fertilizer. To do this we have used Linear Programming (LP) – a technique specifically designed to help managers make decisions relative to the allocation of resources. In this case, C-30 = , C-92 = , D-21 = , and E-11 = . The constraints for this case were translated into linear equations (i.e. inequalities) to mathematically express their meaning. The first constraint that C-11 must constitute for at least 15% of the blend can be expressed as: . The second constraint that C-92 and C-30 must together constitute at least 45% of the blend can be expressed as: . The third constraint that D-21 and C-92 can together constitute no more than 30% of the blend can be expressed as: . Lastly, the fourth constraint is that Quain-Grow is packaged and sold in 50-lb bags can be expressed as: . These equations were obtained and entered into a POM LP as a minimizing function. The objective function of this case was calculated and expressed as . The following table is the input