Question

Consider the following linear program:

Max 3A + 2B

1A+1B<=10

3A+ 1B<=24

1A+2B<=16

A) Run the syntax for the LINDO results.

B) Assume that the objective function coefficient for A changes from 3 to 3.8 and the objective function coefficient for B changes from 2 to 1.2.   Does the optimal solution change? Show the calculation based on 100% rule on objective function.

C) Assume that the right hand side of Constraint 2 changes from 24 to 28 and Constraint 3 changes from 16 to 14.5? Will the dual price change.   Show the calculation based on 100% rules for the right hand side constraints.   What will be the new profit margin based on the dual price changes?

Answer 1

A) LINDO result is following:

Result:

A = 7

B = 3

Objective value = 27

B)

Run the range report on LINDO by pressing CTRL+R , while keeping the curser on LINDO model window. Range report is following:

Using 100% rule, we determine whether the sum of changes in objective coefficients as a ratio of their respective allowable change (allowable increase or decrease as applicable) is >= 100%, in which case, optimal solution would change, otherwise not.

The sum = (3.8-3)/3+(2-1.2)/1 = 1.07 or 107%

The sum is greater than 100%. Therefore, 100% rule is violated. Hence, the optimal solution changes.

C)

The sum = (28-24)/6+(16-14.5)/3 = 1.17 or 117%

100% rule is violated. Therefore, dual price may change. We need to re-run the LINDO model to get the new profit margin

New profit margin = 29