14. Consider the LP sensitivity output below Adjustable Cells Cost SB$2 $C$2 SDS

ID: 357082 • Letter: 1

Question

14. Consider the LP sensitivity output below Adjustable Cells Cost SB$2 $C$2 SDS2 SB$3 $C$3 SDS3 Plant 1 Small Plant 1 Medium Plant 1 Large Plant 2 Small Plant 2 Medium Plant 2 E+30 14.99999998 23.99999996 23.99999996 360 60 516.6666667 166.6666667 666.6666667 39.99999995 23.9999999747 .99999996 9.99999995 14.99999999 39.99999997 39.99999997 420 1E+30 Price R.H. Side Cell SES2 Plant 1 Total Produced SES3 Plant 2 Total Produced SES4 Plant 3 Total Produced BSS Total Produced Smal SCSS Total Produced Medium SS Total Produced Large SIS2 SSpace Used IS3 Space Used SIS4 S 694.4444444 833.3333333 416.6666667 83.3333333 844.4444444 16.6666667 13000 12000 E+30 1E+30 1E+30 1E+30 1E+30 355.5555556 1E+30 383.3333333 55.55555556 66.66665667 33. 33333333 166.6666667 750 13000 888.88888891777.7 12 20 5000 181.8181818 a) (2) What is the optimal objective function value? b) (5) If the objective coefficient for the "Plant 2 Large" variable were changed from 420 to 440, what would the impact on the optimal solution be? On the objective function value? Explain. c) (4) Which constraints are binding constraints? How do you know? d) (4) Ifthe RHS for the "Space Used" constraint is changed from 13000 to 13100, what would the impact on the optimal solution be? On the objective function value? Explain.

Explanation / Answer

14)

a) Objective function value = ?(final value * Objective coefficient)

looking in the Adjustable Cells Table:

Objective function value = 0*300+177.78*360+516.67*420+166.67*300+666.67*360+0*420

Objective function value=

571004.4

b) The allowable increase for ‘Plant 2 Large’ variable is 39.99, if we change the objective coefficient value from 420 to 440; we are increasing it by 20 which are well within the allowable increase limits.

Hence, changing the objective coefficient to 440 will have no effect on the optimal solution value.

Since the final value of the plant 2 large variable is 0, the objective function value will also remain the same.

(please note here the reduced cost for this variable is -39.99, i.e. a change of 39.99 will make the final value for this variable non-zero, which not the case here)

c) Constraints with a slack/shadow price = 0, are binding constraints.

Here, Plant 1 Total Produced, Plant 2 Total Produced, Plant 3 Total Produced, Total Produced Small, Total produced Medium, and the Total Produced Large are binding constraints.

d) Allowable increase for the constraint is 888.89, and the change we are doing is 13100-13000=100, which is less than the allowable increase limits.

The optimal solution thus won’t change.

It has a shadow price of 12, i.e. Increase in 12 units in the RHS, will lead to 1 unit increase in objective function value.

Hence, increase in objective function value = 100/12 = 8.33 units.