The Queen City Nursery manufactures bags of potting soil from compost and topsoil. Each cubic foot of compost costs 12 cents and contains 4 pounds of sand, 3 pounds of clay, and 5 pounds of humus
Each cubic foot of topsoil costs 20 cents and contains 3 pounds of sand, 6 pounds of clay, and 12 pounds of humus. Each bag of potting soil must contain at least 12 pounds of sand, at least 12 pounds of clay, and at least 10 pounds of humus. Formulate the problem as a linear program. Plot the constraints and identify the feasible region. Graphically or with corner points find the best combination of compost and topsoil that meets the stated conditions at the lowest cost per bag. Identify the lowest cost possible.
Let C = cubic feet of compost used per bag of potting soil
Let T = cubic feet of topsoil used per bag of potting soil
Minimize cost = $0.12C + $0.20T
Subject to
4C + 3T ? 12
3C + 6T ? 12
5C + 12T ? 10
C, T ? 0
The panel below contains the graphical and corner-point solutions. The minimum cost per bag is $0.45, and is achieved by using 2.4 cubic feet of compost and 0.8 cubic feet of topsoil.
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