Question

The owner of Tastee Cookies needs to decide whether to lease a small, medium, or large new retail outlet. The owner estimates that monthly profits will vary with demand for cookies as follows: Low - $1000, Medium - $2500, High - $3000. For what range of probability that demand will be high, will the decision be to lease the medium facility?

Answer 1

To determine the range of probability for high demand where the decision to lease the medium facility is favorable, we need to compare the profits from leasing the medium facility to the profits from leasing the small and large facilities. The range of probability is 0.6 < x < 0.75.

Step-by-step explanation:

To determine the range of probability for high demand where the decision to lease the medium facility is favorable, we need to compare the profits from leasing the medium facility to the profits from leasing the small and large facilities. Based on the given information, the monthly profits for low, medium, and high demand are $1000, $2500, and $3000 respectively. To determine the range, we need to find the probability range where the profits from leasing the medium facility are greater than the profits from leasing the small facility but less than the profits from leasing the large facility.

Let's assume x as the probability of high demand. The profit for leasing the medium facility is $2500. The profit for leasing the small facility is $1000, and the profit for leasing the large facility is $3000.

So, we have the inequality: 1000 < x * 3000 + (1 - x) * 1000 < 2500

Simplifying, we find that 0.6 < x < 0.75.