Question 2

A company manufactures two types of products, A and B. Product A requires 2 units of resource X, 1 unit of resource Y, and 3 units of resource Z. Product B requires 1 unit of resource X, 3 units of resource Y, 2 units of resource Z, and 1 unit of resource W. The company has 100 units of resource X, 90 units of resource Y, 120 units of resource Z, and 80 units of resource W. Product A brings in a profit of $5, while product B brings in a profit of $4. How many units of products A and B should the company produce to maximize its profit?

(a) Formulate a linear program for the company to make the decision.
(b) Solve the formulated programming.
(c) If there is no constraint for resource W, what is the optimal solution to the above question?