Chapter B, Problem 1CS

Quain Lawn and Garden, Inc

Bill and Jeanne Quain spent a career as a husband-and-wife real estate investment partnership in Atlantic City, New Jersey. When they finally retired to a 25-acre farm in nearby Cape May County, they became ardent amateur gardeners. Bill planted shrubs and fruit trees, and Jeanne spent her hours potting all sizes of plants. When the volume of shrubs and plants reached the point that the Quains began to think of their hobby in a serious vein, they built a greenhouse adjacent to their home and installed heating and watering systems.

By 2012, the Quains realized their retirement from real estate had really only led to a second career—in the plant and shrub business—and they filed for a New Jersey business license. Within a matter of months, they asked their attorney to file incorporation documents and formed the firm Quain Lawn and Garden, Inc.

Early in the new business’s existence, Bill Quain recognized the need for a high-quality commercial fertilizer that he could blend himself, both for sale and for his own nursery. His goal was to keep his costs to a minimum while producing a top-notch product that was especially suited to the New Jersey climate.

Working with chemists at Rutgers University, Quain blended “Quain-Grow.” It consists of four chemical compounds, C-30, C-92, D-21, and E-11. The cost per pound for each compound is indicated in the following table:

CHEMICAL COMPOUND	COST PER POUND
C-30	$.12
C-30	.09
D-21	.11
E-11	.04

The specifications for Quain-Grow are established as:

1. a. Chemical E-11 must constitute at least 15% of the blend.
2. b. C-92 and C-30 must together constitute at least 45% of the blend.
3. c. D-21 and C-92 can together constitute no more than 30% of the blend.
4. d. Quain-Grow is packaged and sold in 50-lb bags.

Discussion Questions

1. 1. Formulate an LP problem to determine what blend of the four chemicals will allow Quain to minimize the cost of a 50-lb bag of the fertilizer.
2. 2. Solve to find the best solution.