Question

Decision Variables:

B= # of external modems to be produced, profit=$40/unit

P= # of internal modems to be produced, profit=$120/unit

Objective: MaxTotal Profit= Max $40 B + $120 P                  

Constraints:                       

Software Engineer (SE):     20 B + 5 P                             <= 2400 minutes               

QC Manager:                       15 B + 30 P                         <= 2400 minutes               

Demand for B:                    B                                           <= 100   units                    

Demand for P:                    P                                           <= 50     units

QC is the Bottleneck. P is the preferred product since $120/30 > $40/15

Optimal production quantities: B=60, P=50.

Questions:

1. True/False - Allowable Increase in profit for B is $20.

2. True/False - Allowable decrease for profit per unit of P is $40

3. True/False - QC Manager SP: $4 per min

4. True/False - Demand for P:
SP: $120 per unit

5. If:

Software Engineer (SE):     20 B + 5 P                             <= 2010 minutes               

QC Manager:                       15 B + 30 P                         <= 4000 minutes  

Then: True/False - Demand for P:
SP: $110 per unit

Answer 1

We have to find the Allowable increases for profit per unit of B, allowable decrease for profit per unit of P, Shadow Price for QC manager and Shadow price for Demand of P. In order to find above parameters, we solve the given problem using the Excel solver and generate a sensitivity report.

The solution is as shown. This is solved using excel solver.

We generate a sensitivity report as shown below. The sensitivity report is generated by clicking on the sensitivity section in Excel solver output window and then clicking OK as shown below:

The sensitivity report extract is shown below:

As seen from the above 2 tables:

1. The Profit for B is in Cell B2. Against B2 in the above sensitivity table, the Allowable Increase is given as 20.

Hence, the statement is given in the question; Allowable Increase for profit per unit of B is $20, is correct

Answer: True

2. The Profit for P is in Cell B3. Against B3 in the above sensitivity table, the Allowable decrease is given as 40.

Hence, the statement is given in the question, Allowable decrease for profit per unit of P is $40 is correct

Answer: True

3. The Constraint for QC manager is in Cell B10. Against B10 in the above sensitivity table, the Shadow price is given as 2.667.

Hence, the statement is given in the question, QC Manager SP: $4 per min is incorrect

Answer: False

4. The Constraint for Demand of P is in Cell B12. Against B12 in the above sensitivity table, the Shadow price is given as 40.

Hence, the statement is given in the question, Demand for P SP: $120 per unit is incorrect

Answer: False

Now, if the Constraints are changed,

The solution is as shown. This is solved using excel solver.

The revised sensitivity report extract is shown below:

As seen from the above 2 tables, the Constraint for Demand for P is in Cell B12. Against B12, the shadow price is given as 110.

Hence, the statement given in the question, Demand for SP = $110 per unit is correct

5. Answer: True.

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