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Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919

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Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919
Textbook Problem
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Market Analysis A sporting goods company has decided on two possible cities in which to open a new store. Management estimates that City 1 will yield $20 million in revenues if successful and will lose $4 million if not. whereas City 2 will yield $50 million in revenues if successful and will lose $9 million if not. City 1 has a 0.3 probability of being successful and City 2 has a 0.2 probability of being successful. In which city should the sporting goods company open the new store with respect to the expected return from each store?

To determine

To calculate: In which city should the sporting goods company open the new store with respective to the expected return from each store.

Explanation

Given Information:

City 1 will yield 20 million in revenues if successful and will lose $4 million if not and city 2 will yield 50 million in revenues if successful and will lose $9 million if not. The probability of being successful of city 1 has 0.3 and the probability of being successful of city 2 has 0.2.

Formula Used:

If x1 be the gain of successful with probability p(x1) and x2 be the loss of failure with probability p(x2) then

E(x)=x1p(x1)x2p(x2)

Step-1: Find the expected value of the city 1 and city 2.

Step-2: Compare which one amount is more.

Calculation:

Consider the given conditions for City 1

x1=20millionx2=$4millionp(x1)=0.3p(x2)=10.3

And,

p(x2)=0.7

Now, apply the formula to find the probability

E(x)=x1p(x1)x2p(x2)=20(0

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