Below is the computer solution to a linear programming problem linear programmin

Question

Below is the computer solution to a linear programming problem linear programming:   

Note:  The Reduced Cost is often referred to as the Coefficient Sensitivity.

For the above information, answer the following questions.  Provide your answers based on the above information and explain your answers in terms of this information.  

a)  What are the objective function and the constraints?

b)  What are the values of the variables at optimality and what is the value of the objective function at optimality?

c)  If there was an opportunity to purchase additional units of each resource (as expressed by the constraints), based on the sensitivity analysis which resource(s) would you consider for purchase?  Why?  Identify all of the resources that you would consider.  If you did not consider a resource, why did you exclude it?  Remember that Constraint 1 is equivalent to Resource 1, Constraint 2 is Resource 2, and Constraint 3 is Resource 3.   

d)  Suppose the contribution of variable X2 in the objective function increases by 10.  What are the values of the variables at optimality now and what is the value of the objective function at optimality

X1 X2
RHS Shadow Price Maximize 40 30


Constraint 1 0.4 0.5 <= td="">   20 33.3333 Constraint 2 0.0 0.2 <= td="">   5 0 Constraint 3 0.6 0.3 <= td="">   21 44.4444 Solution 25 20








Sensitivity   Analysis





Variable Value Reduced Cost Original Value Lower Bound Upper Bound X1 25 0 40 24 60 X2 20 0 30 20 50





Constraint Shadow Price Slack/ Surplus Original Value Lower Bound Upper Bound Constraint 1 33.3333 0 20 14.00 21.50 Constraint 2 0 1 5 4.00 Infinity Constraint 3 44.4444 0 21 18.75 30.00

Explanation / Answer

a. Z=40X1+30X2

0.4 x1+0.5x2<=20
0.2x2<=5

0.6x1+0.3x2<=21
b. x1=25 x2=20

therfore, z=40x1+30x2= 40*25+30*20=1600

c. resource 2 ,

d. 6=x1, 15=x2 z=40*6+30*15=690

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