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I have the answer to and the sensitivity analysis for a LP maximization problem. (See picture)

http://postimg.org/image/xs4iowbrj/

How can I deduce the original LP problem?

I have figured out this:

Max Z = 5x1 + 4x2 + 3x3 + 4x4

a1x1 + b1x2 + c1x3 + d1x4 <= 40

a2x1 + b2x2 + c2x3 + d2x4 <= 30

But I don't know how to deduce a1...d2. Thanks

tsorn
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  • I dont´t think, that you have only these tables. What is the original exercise ? – callculus42 Aug 01 '15 at 15:56
  • This is the original exercise. It is possible, and if I remember correctly you have to use "final value" under "variable cells" in the sensitivity analysis (first picture) along with the shadow price. – tsorn Aug 01 '15 at 16:03
  • But there should be a problem described. For example, what does "produksjon:kaffekaker" mean ? Is it the amount of produced coffee named kaker ? What is the context ? Keep in mind, that we have only the linked pictures-nothing else. – callculus42 Aug 01 '15 at 16:12
  • I'm sorry, I uploaded the wrong picture.

    This is an exam problem, and there is no other given context. Not that it matters anyway; all excel sensitivity analysis are in the same format.

     – tsorn Aug 01 '15 at 16:25

1 Answers1

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It is indeed possible. I'm getting close, but I need help the rest of the way.

I'm able to find the constants for one of the constraints using reduced cost and shadow price from the sensitivity report. Lets redefine our problem so it becomes clearer:

Max Z = 5x1 + 4x2 + 3x3 + 4x4

a11*x1 + a12*x2 + a13*x3 + a14*x4 <= 40

a21*x1 + a22*x2 + a23*x3 + a24*x4 <= 30

Let y1 and y2 be the shadow price for constraints 1 and 2.

Let r1..r4 be the reduced cost for x1..x4.

Let c1..c4 be the constants for the max problem (here 5, 4, 3, 4).

Then:

r1 = c1 - (a11*y1 + a21*y2)

r2 = c2 - (a12*y1 + a22*y2)

and so on. (Source page 80)

Since the shadow price is 0 for constraint 1 (y1=0) this gives

a21 = 6, a22=4, a23=4, a24=4

The second constraint then becomes

6*x1 + 4*x2 + 4*x3 + 4*x4 <= 30

How can I find the constants for the first constraint?

(According to the exam solution, it's supposed to be a11..a14 = 4, 6, 4, 2)

tsorn
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