Question

16. 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 High Medium 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 S7,000 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.

Answer the following questions using the information provided above

8. Which constrains are binding?

9. If we can decrease the demand of high-grade aluminum by 2 tons at the cost of $1000/ton, is it worth doing this? And why?

10. If the demand of medium-grade aluminum increases by 4 tons, what is the new total cost? And why?

Answer 1

Answer:

16) Suppose X denotes the number of days to operate Mill 1

and Y denotes the number of days to operate Mill 2

Let the Mill 1 be operated for x days and Mill 2 for y days.

Objective function is for minimising cost

Minimise Z = 6000X +7000Y

Subject to.

$6X+2Y \geq 12$

$2X+2Y \geq 8$

$4X+10Y \geq 5$

$X,Y \geq 0$