The Queen City Nursery Manufactures Bags of Potting Soil from Compost

The Queen City Nursery manufactures bags of potting soil from compost and topsoil. Each cubic foot of compost costs 20 cents and contains 4 pounds of sand, 3 pounds of clay, and 5 pounds of humus. Each cubic foot of topsoil costs 30 cents and contains 3 pounds of sand, 5 pounds of clay, and 7 pounds of humus. Each bag of potting soil must contain at least 12 pounds of sand, at least 15 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.