The owner of Tastee Cookies needs to decide whether to lease a small,medium,or large new retail outlet.She estimates that monthly profits will vary with demand for her cookies as follows:
For what range of probability that demand will be high,will she decide to lease the medium facility?

Question

The owner of Tastee Cookies needs to decide whether to lease a small,medium,or large new retail outlet.She estimates that monthly profits will vary with demand for her cookies as follows:
 For what range of probability that demand will be high,will she decide to lease the medium facility?

Quizplus · Accepted Answer

To determine whether the owner should lease the medium facility, we need to find the range of probabilities in which demand will be high, and for which the monthly profits from the medium facility will be greater than those from the small facility, but less than or equal to those from the large facility.

Let P(demand is high) = p

The monthly profits for each facility are as follows:

Small facility: $3,000
Medium facility: $5,000 + $1,000p
Large facility: $9,000 + $500p

The owner will choose the medium facility if:

$5,000 + $1,000p > $3,000     (profits from medium facility > profits from small facility)

$5,000 + $1,000p ≤ $9,000 + $500p   (profits from medium facility ≤ profits from large facility)

Simplifying these inequalities, we get:

0.33 ≤ p ≤ 0.5

Therefore, the range of probabilities in which the owner should lease the medium facility is between 0.25 and 0.5, or answer choice C.

The Owner of Tastee Cookies Needs to Decide Whether to Lease