Problem $12-07$

Manson Inn is a $96-$room hotel located near the airport and convention center in Louisville, Kentucky. When a convention or a special event is in town, Marson increases ta normal room rates and lakes reservations

based on a revenue management system. The Classic Corvette Owners Assocarbon scheduled its annual convention in Louisville for the first weekend in June, Hanson Inn agreed to make at least $50\%$ of its rooms

available for convention attendees at a special convention rate in order to be listed as a recommended hotel for the convention. Although the majority of attendees at the annual meeting typically request a friday and

Saturday two$-$raght package, some attendees may select a Friday night anty or a Saturday night only reservation. Customers not attending the convention may also request a Friday and Saturday two$-$night package,

or make a Friday night only or Saturday night only reservation. Thus, six types of reservations are possible: convention customers$/$two$-$night package; convention customers$/$Friday night only; convention

customers$/$Saturday night only; regular customers$/$twc$-$night package; regular customers$/$Friday night only; and regular customers$/$Saturday night only.

The cost for each type of reservation is shown henk.

Two$-$Night Package

$5225$

Regular

Friday Night

Only

$$123$

$$146$

Saturday Night Only

$$1305152$

The anticipated demand for each type of reservation is as follows:

Two$-$Night Package

$40$

$20$

Coevemion

Regulat

Friday Night Only

$20$

$30$

Saturday Night Only $15$

$25$

Manson Inn would like to determine how many rooms to make available for each type of reservation in order to maximize totar revenue.