Consider the following linear programming problem, which maximizes profit for two products: regular (R) and super (S):

MAX 5R + 75S

s.t.

1.2 R + 1.6 S ≤ 600 assembly (hours)

0.8 R + 0.5 S ≤ 300 paint (hours)

0.16 R + 0.4 S ≤ 100 inspection (hours)

R, S = 0

See the sensitivity report provided below:

The upper limit of the regular product (R) objective function coefficient (profit of R) is _________ .

Please choose the option that best fit the empty space above.

Question

Consider the following linear programming problem, which maximizes profit for two products: regular (R) and super (S):

MAX 5R + 75S

s.t.

1.2 R + 1.6 S ≤ 600  assembly (hours)

0.8 R + 0.5 S ≤ 300    paint (hours)

0.16 R + 0.4 S ≤ 100    inspection (hours)

R, S  >= 0

See the sensitivity report provided below:

The upper limit of the regular product (R) objective function coefficient (profit of R) is _________ .

Please choose the option that best fit the empty space above.

BlackTom AI · Accepted Answer

The allowable increase in a sensitivity report gives how much the current objective coefficient can rise while the current optimal basis remains valid. Here the Regular product R currently has objective coefficient 5 and an Allowable Increase of 25, so its upper limit is 5 + 25 = 30.

1) Relevant knowledge points and concepts
- Sensitivity (post-optimal) analysis: “Allowable Increase” for an objective coefficient is the amount it can increase before the optimal basis changes.
- For a nonbasic variable, the reduced cost shows how much the coefficient must improve to enter the basis; when the coefficient increases by the allowable amount the reduced cost reaches zero and the variable can become basic.

2) Step-by-step reasoning
- Read the sensitivity report row for Regular (R): Objective Coefficient = 5, Allowable Increase = 25, Allowable Decrease = 1E+30 (practically unlimited).
- The upper bound on the coefficient = current coefficient + allowable increase.

3) Calculations (all intermediate steps)
- Current coefficient of R = 5
- Allowable increase = 25
- Upper limit = 5 + 25 = 30

4) Why the correct answer is correct
- The sensitivity report explicitly gives the allowable increase for R as 25. Adding that to the current coefficient 5 gives 30; the optimal basis remains valid for any R profit up to 30. If R’s profit exceeded 30 the basis could change.

5) Why the other options are incorrect
- Options listed (120, 20, 40, 70) do not equal 30, so none match the upper limit implied by the sensitivity report. 20 is less than the current 5+allowable decrease logic, 40 and 70 are greater than 30 and not supported by the report, 120 is far off.

6) Conclusion
- The upper limit for R’s objective coefficient is 30, which is not among the given numeric choices; therefore “None of the above” is the correct selection. This matches the provided answer.

类似问题

OPTIMIZATION AND EXCEL SOLVER Following is the Sensitivity Report of an Excel Solver Optimization problem. This is a revenue maximization problem. What is the impact of increasing the quantity of silk by 10 units?

Using the data from the example in class, conduct sensitivity analysis to PRICE. Assume tax rate of 21%. What is the projected NI at the lower price level?

Which of the following is NOT a question answered by standard sensitivity analysis information?

The upper limit of the third coefficient of the objective function is _________ .

Answer the following statement with TRUE or FALSE: the correct way to implement a sensitivity analysis for the second coefficient of the objective function is to vary the second coefficient and the next one at the same time (eg.: coefficient #2 and #3).

Suppose r=12 and d=21. Then, the optimal solution is (Ryegrass, Orchard grass) = (4,0) is optimal. What is the allowable increase associated with d? If your answer is infinity, enter "999".

Suppose r=150 and d=150. Which of the following actions (taken individually) would cause the new optimal solution to change? (Select all that apply.)

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