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Chapter 5: Q. 5.6 (page 217)

Your company must make a sealed bid for a construction project. If you succeed in winning the contract (by having the lowest bid), then you plan to pay another firm $100,000 to do the work. If you believe that the minimum bid (in thousands of dollars) of the other participating companies can be modeled as the value of a random variable that is uniformly distributed on (70,140), how much should you bid to maximize your expected profit?

Short Answer

Expert verified

The maximum profit to be expected is40/7thousands of dollars

Step by step solution

01

Evaluate E(P)

The lowest bid's density function is

f(x)=1140-70

Otherwise, it is equal to zero for x鈭�(70,140). Let's say we invest xthousand dollars in our offer. We will make a profit of (x-10)thousand dollars if our bid wins the competition. In that instance, the profit that can be expected is

E(P)=(x-100)脳140-x70=170240x-x2-14000

02

Find Maximum profit

Let's discover a value for xthat optimizes profit. We have that with distinguishing.

ddxE(P)=170(240-2x)=0

This means that x=120. As a result, the highest profit

E(P)x=120=(120-100)脳140-12070=407

thousand of dollars.

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