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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 Repeat Exercise 37 for the case in which the probabilities of City 1 and City 2 being successful are 0.4 and 0.25, respectively.

Market Analysis A sporting goods company has decided on two possible cities in which to open a new store. Management estimates that City I 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 I 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: The city where the sporting goods company shall open its new business and the expected return from each store. The city 1 not successful then will lose $4million and if successful yields $20million in revenue. For city 2 not successful then will lose $9million and if successful yields $50million in revenue.

Explanation

Given Information:

For the sporting goods company city 1 has a 0.4 chance of being successful and city 2 has a

0.25 chance of being successful.

Formula used:

Let the probability for occurring an event be P(x),

Then the probability of not-occurring the event is P(x¯)=1P(x).

If the company yields $amillion when successful and loses $bmillion when not, then the

The total profit is,

Profit=aP(successful)bP(notsuccessful)

Where,

P(successful)=Probabilityofcompanybeingsuccessful

P(not-successful)=1P(successful)

Calculation:

Consider the given data.

For city 1,

P(city1issuccessful)=0.4P(city1isnot-successful)=10

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