1. United Aluminum Company of Cincinnati produces three grades (high, medium, an

Question

1. 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 2 High Medium Low 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 operate each mill in order to meet the contract at the minimum cost. Formulate a linear programming model for this problem. If the optimal solution is to run Mill 1 for 4 days and Mill 2 for 0 days, How much extra (i.e., surplus) high-, medium-, and low-grade aluminum does the company produce at the optimal solution? a. b.

Explanation / Answer

(a)

Let the number of days mill 1 is operated be x

Let the number of days mill 2 is operated be y

We need to minimize the cost, i.e. 6000x + 7000y,

given the condition that,

6x + 2y >= 12 [High Grade Aluminium]

2x + 2y >= 8 [Medium Grade Aluminium]

4x + 10y >= 5 [Low Grade Aluminium]

(b)

If the optimal solution is x = 4 and y = 0

So, the high grade aluminium produced = 6x = 24 tonnes

i.e. 24-12 = 12 tonnes surplus

the medium grade aluminium produced = 2x = 8 tonnes

i.e. 8-8 = 0 tonnes surplus

the low grade aluminium produced = 4x = 16 tonnes

i.e. 16-5 = 11 tonnes surplus

Related Questions

Navigate

• Browse (All)
• Browse 1
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.