A company manufactures three products, A, B, C. The sales volume for A is at least 50% ofthe 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 available is 240 lb. The usage rates of the raw material are 2 lb per unit of A, 4 lb per unit of B, and 3 lb per unit of C. The unit prices for A, B, and C are $20, $50, and $35, respectively.
a. Formulate the Linear Program.
b. Use the simplex algorithm and determine the optimal product mix for the company.
c. Determine the values for the dual variables from the final simplex tableau.