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.

Chemical Compound Cost per Pound

C- 30 .......... $.12

C- 92 ......... .09

D- 21 ......... .11

E- 11 .......... .04

The specifications for Quain- Grow are established as:

a) Chemical E- 11 must constitute 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) Quain- Grow is packaged and sold in 50- lb bags.

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. Solve to find the best solution.