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.
Solve this problem by showing your work as described in the followings. Upload your work in pdf file format.
1. Formulate the problem as a linear program.
2. Plot the constraints and show the feasible region and corner points.
3. Identify the optimal solution.
4. Interpret the optimal solution.