A company produces two products made from aluminum and copper. The table below gives the unit…

A company produces two products made from aluminum and copper. The table below gives the unit requirements, the unit production man-hours required, the unit profit and availability of the resources (in tons).

Aluminum

Copper

Man-hours

Unit profit

Product 1 (X1)

1

0

2

50

Product 2 (X2)

1

1

3

60

Available

10

6

24

The problem was solved by the Solver giving the following output:

Optimal Objective Value = 540.00000

Variable

Value

Reduced Cost

X1

6.00000

0.00000

X2

4.00000

0.00000

Constraint

Slack/Surplus

Dual Value

1

0.00000

30.0000

2

2.00000

0.0000

3

0.00000

10.0000

Variable

Objective Coefficient

Allowable Increase

Allowable Decrease

X1

50.00000

10.0000

10.0000

X2

60.00000

15.0000

10.0000

Constraint

RHS Value

Allowable Increase

Allowable Decrease

1

10.00000

2.00000

1.00000

2

6.00000

Infinite

2.00000

3

24.00000

2.00000

4.00000

  1. What is the optimal production schedule?
  2. Within what range for the profit on product 2 will the solution in (a) remain optimal? What is the optimal profit when C2 = 70?
  3. Suppose that the unit profits on X1 and X2 changed simultaneously from 50 to 55 and 60 to 65, respectively. Would the optimal solution change? Explain.
  4. Explain the meaning of the “Dual Values” column. Given the optimal solution, why should the dual value for copper be 0?
  5. What is the increase in the value of the objective function for an extra unit of aluminum?
  6. Man-hours were not figured into the unit profit as it must pay three workers for eight hours of work regardless of the number of man-hour used. What is the dual price for man-hours? Interpret.
  7. On the other hand, aluminum and copper are resources that are ordered as needed. The unit profit coefficients were determined by: Selling price per unit – Cost of the resources per unit. The 10 units of aluminum cost the company $100. What is the most the company should be willing to pay for extra aluminum?

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