Consider the Linear Programming formulation and its associated MS Excel solution
ID: 3141966 • Letter: C
Question
Consider the Linear Programming formulation and its associated MS Excel solution below. Max Time 100 sec, Irerations 100, Precision 0.000001 Max Subproblems Unlimited, Max Integer Sols Unlimited, Integer Tolerance 5 Carefully examine the MS Excel output above. The dual price associated with constraint two is 0.67. If the right hand side of constraint two is increased by 5 units (i.e., 5x_1 + 4x_2 > = 40 becomes5x_1 + 4x_2 > = 45) what impact does this have on the optimal objective function value of z = 82.67? Specifically, show any calculations to get a revised z-value. Similarly, suppose that the right hand side of constraint two is decreased by three (3) units. What impact does the aforementioned change have on the objective function value of z = 82.67? Specifically show any calculations to get a revised z-value.Explanation / Answer
First of all the function written in the right side which has to be minimized is not matching with this problem.
With x1 = 5.333 & x2 = 3.333, the objective value is 49.333
According to me, the objective function here is 8x1 + 12x2
I will be answering the question with this correction
Part (a) - Increase the RHS of constraints 2 by 5, making it 45 from 40
It will change the final variable values and hence the objectve function.
x1 = 7, x2 = 2.5, & z = 86.
When the RHS is increased by 5 points, it has be adjusted in adjusted in the variable with lower coefficient in the objective function which is X1
Also when X1 is increased, it open a possibility to reduce x2 (which has coeff 12 in objective) further down which was capped high earlier due to constraint 3.
However in this whole change, minimum z value achieved has moved to 86 from 82.67
Part (b) - Decrease the RHS of constraints 2 by 5, making it 37 from 40
x1 = 4.333333, x2 = 3.833333, & z = 80.66666667.
Reducing the RHS of constraint 2, provides with an opportunity to reduce X1 or X2.
If X2 is reduced, again contraint 3 will start facing problem making the LHS at least 12. That is why X1 has been reduced and to make up for it X2 has been increased.