Question: 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.

MILL

Aluminum

Grade__________1_________2___

High 6 2

Medium 2 2

Low 4 10

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 operated each mill in order to meet the contract at the minimum cost.

Formulate a linear programming model for this program.