A company produces two products requiring resources P and Q. Management wants to determine how many units of each product to produce so as to maximize profit. For each unit of product 1, 1 unit of resource P and 2 units of resource Q are required. For each unit of product 2, 3 units of resource P and 2 units of resource Q are required. The company has 200 units of resource P and 300 units of resource Q. Each unit of product 1 gives a profit $1, and each unit of product 2, up to 60 units, gives a profit of $2. Any excess over 60 units of product 2 brings no profit, so such an excess has been ruled out.
(a) Formulate a linear programming model for this problem.
(b) Solve this problem graphically. What is the resulting total profit?