I need help with B-F, please! I dont need help with A

A) 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 shown below. 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. Define x₁ as the number of operation days for mill 1, x₂ as the number of operation days for mill 2, and Z as the total cost. Which of the following model formulations is correct?

Group of answer choices

Maximize Z=6000x1+7000x2 s.t. 6x1+2x2>=12 2x1+2x2>=8 4x1+10x2>=5 x1, x2>=0

Maximize Z=6000x1+7000x2 s.t. 6x1+2x2=0

Minimize Z=6000x1+7000x2 s.t. 6x1+2x2=0

Minimize Z=6000x1+7000x2 s.t. 6x1+2x2>=12 2x1+2x2>=8 4x1+10x2>=5 x1, x2>=0

B) Solve the previous formulated model (United Aluminum Company) by using Excel and POM-QM, the optimal solution is

Group of answer choices

x1=0, x2=4

x1=4, x2=0

x1=1.25, x2=0

x1=0, x2=1.25

C) Solve the previous formulated model (United Aluminum Company) by using Excel and POM-QM, the shadow price for contract requirement of high grade is

Group of answer choices

0

1,000

2,000

3,000

D) Solve the previous formulated model (United Aluminum Company) by using Excel and POM-QM, the sensitivity range for objective function coefficient of x1 (or mill 1), is

Group of answer choices

[1000, 6000]

[6000, infinite]

[0, 7000]

[-6000, 0]

E) Solve the previous formulated model (United Aluminum Company) by using Excel and POM-QM, the sensitivity range for medium grade constraint quantity value is

Group of answer choices

[8, 12]

[8, infinite]

[-4, 4]

[4, infinite]

F) For the previous problem (United Aluminum Company), if the contract requirement for high-grade aluminum increases from 12 tons to 20 tons, what would happen to the optimal solution?

Group of answer choices

The optimal solution would be the same as before, i.e., x1=4, x2=0

The optimal solution would change, i.e., x1=4, x2=4

The optimal solution would change, i.e., x1=2, x2=8

The optimal solution does not exist