$y=4x+190,000$

$(2)$ Hendel Fitness Center is an established fitness center in Minneapolis, Minnesota. While they have been doing reasonably well so far, they believe that they can improve their profits if they add a facility to the center.

Mr$.$ Brian Liu, the resident operations manager in charge of the center, is assessing the impact of adding either one of three facilities to the center: Childcare facility, Indoor Swimming Pool, or Food Court. The additional profits would depend on the increase in enrollments of members. Brian believes that the demand $($based on enrollment$)$ could be Poor, Moderate, or High. The anticipated increase in annual profits for each of these three alternatives under each of the three possible future scenarios are summarized in the table below.

$($a$)$ If Brian predicts that the probabilities for High Demand or Poor Demand are respectively, $0\mathrm{.}6$ and $0\mathrm{.}2,$ which alternative should he choose based on the Expected Monetary Value criterion? Childcare Facility

$($b$)$ Assuming that Brian cannot estimate the probabilities, which alternative is suggested under the following decision rules:

$($I$)$ Maximin

Swiming