Introduction to Management Science 12th Edition by Bernard Taylor

تمرين 65

Solve the linear programming model formulated in Problem for United Aluminum Company graphically.
a. How much extra (i.e., surplus) high-, medium-, and low-grade aluminum does the company produce at the optimal solution
b. What would be the effect on the optimal solution if the cost of operating mill 1 increased from $6,000 to $7,500 per day
c. What would be the effect on the optimal solution if the company could supply only 10 tons of high-grade aluminum
Problem
United Aluminum Company of Cincinnati produces three grades (high, medium, and low) of aluminum at two mills. Each mill has a different production capacity (in tons per day) for each grade, as follows:
The company has contracted with a manufacturing firm to supply at least 12 tons of high-grade aluminum, 8 tons of medium-grade aluminum, and 5 tons of low-grade aluminum. It costs United $6,000 per day to operate mill 1 and $7,000 per day to operate mill 2. The company wants to know the number of days to operate each mill in order to meet the contract at the minimum cost.
Formulate a linear programming model for this problem.