Mary Smith makes pottery by hand in her basement. She has 20 hours available ...

Mary Smith makes pottery by hand in her basement. She has 20 hours available each week to make bowls and vases. A bowl requires 3 hours of labor, and a vase requires 2 hours of labor. It requires 2 pounds of special clay to make a bowl and 5 pounds to produce a vase; she is able to acquire 35 pounds of clay per week. Mary sells her bowls for $50 each and her vases for $40 each. She wants to know how many of each item to make each week to maximize her revenue.
 

a. Formulate an integer programming model for this problem.
b. Solve this model using the computer.
c. Compare the solution in part (b) with the solution without integer restrictions and indicate if the rounded –down solution would have been optimal.
d. Illustrate (c) graphically.