United Aluminum Company of Cincinnati produces three grades

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.

Solution

First tabulate all the information given as follows:

If x is the no of days by mill I, and y is the no of days by mill II, then

the constraints are 6x+2y<=12, 2x+2y<=4 and 4x+10y<=5

The objective is to minimise cost

Total cost z= 6000x+7000y

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Let us solve algebraically these constraints.

We get two solutions as (1.25,0) and (0,0.5)

		Mill	Total	available
Alum grade	I	II
High	6	2	8	12
Medium	2	2	4	8
Low	4	10	14	5
Operat.cost	6000	7000