Shadow price (constraint 1) | Business & Finance homework help

There is a letter on 20 of the values in the sensitivity report. Choose one of the letters and explain what that number means with respect to the solved model. When you post your solution, please title your response “Letter ?” replacing the question mark with the letter you have chosen from the file. Please ensure you do not duplicate a response from a fellow student.

 reply…Q

D13, i.e., Shadow Price (Constraint 1)

The shadow price for Constraint 1 is 0.5. The table shows the range for the right-hand side of a constraint where the shadow price remains unchanged.

So, as long as the right-hand side of constraint 1 is between 33 (lower limit) and 150 (upper limit), the shadow price of 0.5 will apply. Shadow price here refers to the amount of change in optimal objective function value per unit increase in the RHS of a constraint.

So, what will happen to optimal profit if the RHS constraint 1 increases by 50. Considering this is within the limit, this increase is allowable. Therefore the optimal profit will change by 50 (amount of change) times 0.5 (shadow price), i.e., 50 *0.5 =25. Hence, the profit will increase by 25 to become 85.8 (60.8 + 25).

So, what will happen if RHS constraint 1 decreases by 10 (30), then since the allowable decrease is 7, the decrease of 10 is not allowable, and shadow price is not applicable now. In this case, we need to resolve the model.

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