Academic Integrity: tutoring, explanations, and feedback — we don’t complete graded work or submit on a student’s behalf.

Microsoft Excel 14.0 Sensitivity Report Variable Cells Final Reduced Objective A

ID: 399519 • Letter: M

Question

Microsoft Excel 14.0 Sensitivity Report

Variable Cells

Final

Reduced

Objective

Allowable

Allowable

Cell

Name

Value

Cost

Coefficient

Increase

Decrease

$B$4

Units Producted Brand 1

8.4

0

2

2

0.5

$C$4

Units Producted Brand 2

4.8

0

3

1

1.5

Constraints

Final

Shadow

Constraint

Allowable

Allowable

Cell

Name

Value

Price

R.H. Side

Increase

Decrease

$D$9

Ingredient C Left Hand Side

4.2

0

1.5

2.7

1E+30

$D$7

Ingredient A Left Hand Side

90

0.24

90

45

30

$D$8

Ingredient B Left Hand Side

48

0.2

48

24

13.5

a. For the optimal solution, how much should we buy for the brand 1 and brand 2?

b. How much ingredient A is used in actual?

c. What is max upper limit of ingredient B as the shadow price remains as 0.2?

d. Will the cost change if the ingredient C changes to 3 kg?

Microsoft Excel 14.0 Sensitivity Report

Variable Cells

Final

Reduced

Objective

Allowable

Allowable

Cell

Name

Value

Cost

Coefficient

Increase

Decrease

$B$4

Units Producted Brand 1

8.4

0

2

2

0.5

$C$4

Units Producted Brand 2

4.8

0

3

1

1.5

Constraints

Final

Shadow

Constraint

Allowable

Allowable

Cell

Name

Value

Price

R.H. Side

Increase

Decrease

$D$9

Ingredient C Left Hand Side

4.2

0

1.5

2.7

1E+30

$D$7

Ingredient A Left Hand Side

90

0.24

90

45

30

$D$8

Ingredient B Left Hand Side

48

0.2

48

24

13.5

Explanation / Answer

Ans a)

For the optimal solution, we should buy 8.4 units of Brand 1 and 4.8 units of Brand 2.

Ans b)

90 units of ingredient A are used in actual. It can be seen from the final value column of the constraints table.

Ans c)

Ingredient B has an allowable increase of 24 at a shadow price of 0.2. Hence the max upper limit of ingredient B is the sum of the final value of ingredient B and the allowable increase, i.e. 48 + 24 = 72 units.

Ans d)

The allowable decrease of ingredient C is 1E+30 or 1030 and the shadow price is 0. Hence if the ingredient C changes to 3 kg, the value of the objective function (cost) will not change.

This is because a decrease of 1.2 kg in the final value of ingredient C falls within the allowable decrease.