A company produces three products, A, B, and C. The sales volume for A is at least

50% of the total sales of all three products. However, the company cannot sell more than 75 units of A per day. The three products use one raw material, of which the maximum daily availability is 240 lb. The usage rates of the raw material are 2 lb per unit of A,4 lb per unit of B, and 3lb per unit of C. The unit prices for A, B, and Care $20, $50, and $35, respectively.

(a) Determine the optimal product mix for the company.

(b) Determine the dual price of the raw material resource and its allowable range. If available raw material is increased by 120 lb, determine the optimal solution and the change in total revenue using the dual price.

(c) Use the dual price to determine the effect of changing the maximum demand for product A by ±10 units.