**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?

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