Problem 4S-4 A product engineer has developed the following equation for the cos

Question

Problem 4S-4 A product engineer has developed the following equation for the cost of a system component: C (10P2, where C is the cost in dollars and P is the probability that the component will operate as expected. The system is composed of 3 identical components, all of which must operate for the system to operate. The engineer can spend $259 for the 3 components. What is the largest component probability that can be achieved? (Do not round your intermediate calculations. Round your final answer to 4 decimal places.) Probability

Explanation / Answer

Cost of a system component C=(10P)2

Engineer can spend $259 for the three component

Cost of 3 component = 3*(10P)2 = Selling of component

3*(10P)2 =259

(10P)2 =259/3

100 P2 = 86.3333

P=0.9291

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