Question 1

Working with chemists at Virginia Tech and George Washington Universities, landscape contractor Kenneth Golding blended his own fertilizer, called "Golding-Grow." It consists of four chemical com- pounds, C-30, C-92, D-21, and E-11. The cost per pound for each compound is indicated as follows:

Chemical

Compound

Cost Per

Pound ($)

C-30

0.12

C-92

0.09

D-21

0.11

E-11

0.04

The specifications for Golding-Grow are as follows: (1) E-11 must constitute at least 15% of the blend; (2) C-92 and C-30 must together constitute at least 45% of the blend; (3) D-21 and C-92 can together constitute no more than 30% of the blend; and (4) Golding-Grow is packaged and sold in 50-pound bags.

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. (5 marks)

2.Find the optimal point and cost. (5 marks)