Suppose your firm produces two products: A and B. You sell each product for $5. To produce A and B you need to use copper and zinc.

i.

Your firm cannot produce more than 120 units of product A.

ii.

Your firm cannot produce more than 150 units of product B.

iii.

Both product A and B use copper in the production process. To produce one unit of product A, you need 3 units of copper. To produce one unit of product B, you need 6 units of copper. You have a total of 600 units of copper.

iv.

Both product A and B use zinc in the production process. To produce one unit of product A, you need 10 units of zinc. To produce one unit of product B, you need 10 units of zinc. You have a total of 2,000 units of zinc.

a.

Draw the feasible region in a graph.

b.

To maximize profit how many product A and B you need to produce? (what is the

optimal solution) Show optimal solution in the graph and solve mathematically.

c.

What is the maximum profit your firm will make?

d.

Suppose now the price of product A decreases to $1. What is the optimal production? What is the maximum profit?