Problem

Golding Landscaping and Plants, Inc.

Kenneth and Patricia Golding spent a career as a husband-andwife real estate investment partnership in Washington, DC. When they finally retired to a 25-acre farm in northern Virginia's Fairfax County, they became ardent amateur gardeners. Kenneth planted shrubs and fruit trees, and Patricia spent her hours potting all sizes of plants. When the volume of shrubs and plants reached the point that the Goldings 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 2005, the Goldings realized that their retirement from real estate had really only led to a second career-in the plant and shrub business-and they filed for a Virginia business license. Within a matter of months, they asked their attorney to file incorporation documents and formed the firm Golding Landscaping and Plants, Inc. Early in the new business's existence, Kenneth Golding 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 northern Virginia climate. Working with chemists at George Mason University, Golding blended "Golding-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:

The specifications for Golding-Grow are as follows:

a. Chemical E-11 must comprise at least 15% of the blend.

b. C-92 and C-30 must together constitute at least 45% of the blend.

c. D-21 and C-92 can together constitute no more than 30% of the blend.

d. Golding-Grow is packaged and sold in 50-pound bags.

Discussion Questions

1. Formulate an LP problem to determine what blend of the four chemicals will allow Golding to minimize the cost of a 50-pound bag of the fertilizer.

2. Solve by using Excel to find the best solution.