Question

Variable cells

Cell	Name	Final Value	Reduced Cost	Objective Coefficient	Allowable Increase	Allowable Decrease
$B$6	Activity 1	3	0	30	23	17
$C$6	Activity 2	6	0	40	50	10
$D$6	Activity 3	0	–7	20	7	1E+30

Constraints

Cell	Name	Final Value	Shadow Price	Constraint R.H. Side	Allowable Increase	Allowable Decrease
$E$2	Resource A	20	7.78	20	10	12.5
$E$3	Resource B	30	6	30	50	10
$E$4	Resource C	18	0	40	1E+30	22

What is the allowable range for the objective coefficient for Activity 2?

Multiple Choice

• −10 ≤ A2 ≤ 50

• −44 ≤ A2 ≤ 16

• −4 ≤ A2 ≤ 56

• 30 ≤ A2 ≤ 90

• 20 ≤ A2 ≤ 80

If the coefficient for Activity 3 in the objective function changes to $30, then the objective function value:

Multiple Choice

• will increase by $70.

• is $0.

• will increase by $30.

• will remain the same.

• will increase by an unknown amount.

Which parameter is most sensitive to an increase in its value?

Multiple Choice

• The objective coefficient of Activity 1.

• The objective coefficient of Activity 2.

• The objective coefficient of Activity 3.

• All of the choices are correct.

• None of the choices is correct.

What is the allowable range for the objective function coefficient for Activity 3?

Multiple Choice

• 150 ≤ A3 ≤ ∞

• 0 ≤ A3 ≤ 650

• 0 ≤ A3 ≤ 250

• 400 ≤ A3 ≤ ∞

• 300 ≤ A3 ≤ 500

Answer 1

What is the allowable range for the objective coefficient for Activity 2?

• 30 ≤ A2 ≤ 90

Calculated as:

We look for the allowable increase and decrease for that activity. Objective function range: 40 - 10 to 40 + 50 i.e 30 to 90.

If the coefficient for Activity 3 in the objective function changes to $30, then the objective function value:

• will increase by an unknown amount.

As: the change we are willing to do is beyond the allowable range. We'll have to solve again to see the change in the solution.

Which parameter is most sensitive to an increase in its value?

• The objective coefficient of Activity 3.

Because Final value is 0 and the reduced cost is given. For every one unit increase, the profit will get reduced by the reduced cost amount.

What is the allowable range for the objective function coefficient for Activity 3?

• 0 ≤ A3 ≤ 27