Question

Problem 5S-3 A small building contractor has recently experienced two successive years in which work opportunities exceeded the firm's capacity The contractor must now make a decision on capacity for next year. Estimated profits under each of the two possible states of nature are as shown in the table below. Suppose after a certain amount of discussion, the contractor is able to subjectively assess the probabilities of low and high demand: P (low) = .3 and P (high Construct a graph that will enable you to perform sensitivity analysis on the problem NEXT YEAR'S DEMAND Alternative Do nothing Expand Subcontract Low High $50 $60 20 40 80 70 *Profit in $thousands Over what range of P (high) would the alternative of doing nothing be best? Expand? Subcontract? (Include the indifference probability in your answer ranges. Enter the lower probability in the left answer box and higher probability in the right answer box Round your answers to 2 decimal places.) Optimal Ranges Do nothing Expand Subcontract 0 to 1.00

Answer 1

80 80 60 60 40 40 20 20 0 P(High) A = Do Nothing B Expand C Subcontracting

Let value of P-high be P at which A & C are equal:

Equation of A: 50*(1-p) + 60*p = 50 + 10*p

Equation of C: 40*(1-p) + 70*p = 40 + 30*p

Equating the two:

50 + 10*p = 40 + 30*p

p = 0.5

So, Do nothing is best from 0 to 0.5

Equation of B: 20*(1-p) + 80*p = 20 + 60*p

Equating B & C

40 + 30*p = 20 + 60*p

20 = 30*p

p = 0.67

So, Subcontracting is best from 0.5 to 0.67

Expand is best from 0.67 to 1