Question #42664

As a chemist, Davis Golding blends his own fertilizer, called “Golding-Grow.” It consists of 4 chemical compounds, 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 0.14

C-92 0.1

D-21 0.11

E-11 0.06

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 20% of the blend; and

(4) Golding-Glow is packed and sold in 50-pounds bags.

a) Formulate a 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. Explain clearly how you formulate the constraints.

b) Solve using a computer to find the best solution.

Chemical compound Cost per pound ($)

C-30 0.14

C-92 0.1

D-21 0.11

E-11 0.06

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 20% of the blend; and

(4) Golding-Glow is packed and sold in 50-pounds bags.

a) Formulate a 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. Explain clearly how you formulate the constraints.

b) Solve using a computer to find the best solution.

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