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# Decision Making with Utility Functions and Uncertainty

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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?

#### 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.

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