/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 106 Suppose the owner of a salvage c... [FREE SOLUTION] | 91影视

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Chapter 5: Problem 106

Suppose the owner of a salvage company is considering raising a sunken ship. If successful, the venture will yield a net profit of \(\$ 10\) million. Otherwise, the owner will lose \(\$ 4\) million. Let \(p\) denote the probability of success for this venture. Assume the owner is willing to take the risk to go ahead with this project provided the expected net profit is at least \(\$ 500,000\). a. If \(p=.40\), find the expected net profit. Will the owner be willing to take the risk with this probability of success? b. What is the smallest value of \(p\) for which the owner will take the risk to undertake this project?

Short Answer

Expert verified
a. The expected net profit for \(p = 0.40\) is \$1.6 million, so the owner would be willing to take the risk. b. The smallest value of \(p\) for which the owner will take the risk is approximately \(0.33333\) or \(33.33%\).

Step by step solution

01

Calculate Expected Net Profit for \(p=0.40\)

Substitute \(p=0.40\) into the formula for expected net profit: \( E = p \cdot \$10M + (1 - p) \cdot -\$4M = 0.40 \cdot \$10M + (1 - 0.40) \cdot -\$4M = \$4M - \$2.4M = \$1.6M\). Therefore, the expected net profit is \$1.6 million.
02

Evaluate Owner's Willingness to Take Risk at \(p=0.40\)

The owner is willing to take the risk if the expected net profit is at least \$500,000. Since \$1.6 million is greater than \$500,000, the owner would be willing to take the risk given a \(p\) value of 0.40.
03

Calculate Minimum Value of \(p\) for Owner to Take Risk

The owner will take the risk if the expected net profit reaches at least \$500,000. Therefore, set the expected net profit equal to \$500,000 and solve the equation for \(p\): \( \$500,000 = p \cdot \$10M + (1 - p) \cdot -\$4M\). After solving this linear equation for \(p\), the result is \(p \approx 0.33333\) or \(33.33%\).

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