Using graphical sensitivity analysis, determine the probability for no new bridge for which each alternative would be optimal.

Plot a straight line for each alternaitive . Do this by ploting the payoff for new bridge on the left

New Bridge Built No New Bridge

Alternative capacity A 1 14

for new store B 2 10

C 4 6

where A= small, B = medium, and C= large

Question

Using graphical sensitivity analysis, determine the probability for no new bridge for which each alternative would be optimal.

		New Bridge Built	No New Bridge
Alternative capacity	A	1	14
for new store	B	2	10
	C	4	6

where A= small, B = medium, and C= large

Accepted Answer

axis and the payoff for no new bridge on the right axis and then comnecting the two points . Each line represented profit for the entire range of probability of no new bridge. Because the lines represent profit, the line that is highest fora given value of P(no new bridge) is optimal. Thus, from the graph , you can see that for low valuse of this probability, aternative C is best, and for higher values, alternative A is best (B is never the highest line, so it is never optimal).

The dividing line between the ranges wher C and A are otimal occurs where the two lines intersect. To find that probability, first formulate the equation for each line. To do this, let the intersection with the left axis be the y intercept; the slope equals the right-side payoff minus the left-side payoff.Thus, for C you have 4 +(6 -4)P, which is 4 + 2P For A, 1 (14 - 1)P, which is 1 + 13P. Setting these two equal to each other, you can solve for P:

4 + 2P = 1 + 13P

Solving, P =.27. Therefore, the ranges for P(no new bridge) are

[latex]A: 27 \lt P\leq 1.00[/latex]

B: never optimal

[latex]C: 0 \leq P\lt .27[/latex]

Question 5.SP.2: Using graphical sensitivity analysis, determine the probabil...

This Question has been Answered.

Already have an account?

Login

Related Answered Questions