QUESTION 7 (5 marks total)

The Queen City Nursery manufactures bags of potting soil from compost and topsoil. A manager must decide on the mix of products (compost or topsoil) to produce for the coming week. 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, 12 pounds of clay, and 10 pounds of humus. The Nursery would like to minimize its costs. Lets define this linear programming problem as follows:

X1 = cubic feet of compost to be produced

X2 = cubic feet of topsoil to be produced

1. Determine the objective function for this linear programming problem. (1 mark)

2. List all the constraints for this linear programming problem. (1.5 marks)

3. What is the optimal number of cubic feet of compost and topsoil that this hardware firm needs to produce to minimize costs? (2.5 marks)