# Decision Making with Utility Functions and Uncertainty

See attachment.

ABC Company does subcontracting on government contracts. ABC Company is a small company with limited capital with a utility function described as follows:

U(x) = -x/100-x^2/5,000 for x < -1,000

U(x) = x/100-170 for -1,000 ≤ x ≤ 10,000

U(x) = √x for x > 10,000

Part 1

Suppose ABC Company is considering bidding on a given contract. It will cost $2,000 to prepare the bid. If the bid is lost, the $2,000 cost is also lost. If ABC Company wins the bid, it will make $40,000 and recover the $2,000 bid preparation cost. Suppose ABC Company believes the probability of winning the contract is 0.5 if a bid is submitted. What should it do?

Part 2

What should the probability of winning have to be before ABC Company would submit a bid?

https://brainmass.com/business/managerial-statistics/decision-making-utility-functions-uncertainty-607053

#### Solution Preview

See attachment.

Part 1

U(no bid) = U(0) = 0/100-170 = -$170

U(bid) = 0.5* U(-2,000) + 0.5 * U(40,000) = 0.5 * ...

#### Solution Summary

The solution contains step-by-step analysis of decision making with utility functions and uncertainty by obtaining the utilities for no bid and bid scenarios.