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The Sweet Smell Fertilizer Company markets bags of manure labeled "not less than 60 lb dry weight." The packaged manure is a combination of compost and sewage wastes. To provide good-quality fertilizer, each bag should contain at least 30 lb of compost but no more than 40 lb of sewage. Each pound of compost costs Sweet Smell 5¢ and each pound of sewage costs 4¢. Use the Linear Programming method to determine the least-cost blend of compost and sewage in each bag.

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Answer and Step-by-step explanation:

Let

Compost lb per bag = x1 = 30

Compost cost per lb = 0.05

Sewage lb per bag = x2 = 40

Sewage cost per lb = 0.04

Minimize cost = 0.5 x1 + 0.4 x2

Constraints:

Bags of manure labeled “not less than 60 lb dry weight”

X1 + x2 ≥ 60

X1 ≥ 30

X2 ≥ 40

At x1 = 30 and x2 = 40

C = 0.05(30) + .04(40)

   = 1.5+ 1.6

   =$3.1

At x1= 60 and x2 = 0

C= 0.05(60) + 0.04(0)

  = 3 + 0

  =$3.00

At x1 = 30 and x2= 30

C = 0.05(30) + 0.04(30)

    = 1.5 + 1.2

  =$2.7

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