14. Consider the LP sensitivity output below. Adjustable Cells Objective Coeffic
ID: 358614 • Letter: 1
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14. Consider the LP sensitivity output below. Adjustable Cells Objective Coefficient Cell SBS2 Plant 1 Small sos2 plant 1 Large Cost 23.99999996 Decrease 0 1E+30 1499999998 CS2 Plant 1 Medium S8s3 Plant 2 Smal 360 60 16.6666667 166.6666667 666.6666667 ?39.99999995 800 23.99999997 47.99999996 60 59.9099514 9999999 420 39.99999997 SCS3 Plant 2 Medium 9.99999997 E 30 Constraint Cell SES2 Plant 1 Total Produced6 SES3 Plant 2 Total Produced SESA Plant 3 Total Produced sa$s Total Produced Small $C$5 Total Produced Medium soss Total Produced Large516 6666667 SUS2 Space Used SIS3 5 Space Used SIS4 Space Used Price R.H. Side 694.4444444 833 3333333 416.6666667 83 3333333 844.4444444 1E:30 55.55555556 1E 30 66 666667 450 LE:30 3333333333 701E30 166 6666667 55.5555556 E30 383 3333333 1200 E 30 12 20 13000 888 8888889 177 12000 5000 5000 181 8181818 200 a) (2) What is the optimal objective function value? (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. b) o) (4) Which constraints are binding constraints? How do you know? d) (4) If the RHS for the "s 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
1) Objctive function Value = 0 * 300 + 177.778 * 360 + 516.667 * 420 + 166.667 * 300 + 666.667 * 360 + 0 * 420 = Objctive function Value = 571000.4
2) Since change is +20 which is within allowable limit of 39.999 There will not be any change in optimal solution.
Objctive function Value = 0 * 300 + 177.778 * 360 + 516.667 * 420 + 166.667 * 300 + 666.667 * 360 + 0 * 440 =
Objctive function Value = 571000.4
3) In case of binding constraints, Final value = RHS
So J2, J3 and J4 cell constraints are binding
4) Since allowable limit is 888.87, there will not be any change in the optimal solution.
NEW Objective Function Value = Old value + Shadow Price * Change = 571000.4 + 12 * 100 = 572200.4
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