Consider the Linear Programming formulation and its associated MS Excel solution

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.

Related Questions

Navigate

• Browse (All)
• Browse C
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.