PLEASE SHOW ALL YOUR WORK AND GRAPH . IDENTIFY ALL VARIABLES AS WELL

3) 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. a) Formulate the problem. (5 points)-(if max or min is not specified there will be no partial points will be given) b) Plot the constraints and identify the feasible region. Point out the redundant constraint. (10 points) c) Compute the corner points and find the best combination of compost and topsoil that meets the stated conditions and identify the lowest cost. (5 points) b) Compute any slack or surplus in each of the constraints. (5 points) (Show your work)