A linear programming computer package is needed. Hanson 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, Hanson increases its normal room rates and takes reservations based on a revenue management system. A large profesional organization has 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-night package, some attendees may select a Friday night only 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/two-night package; regular customers/Friday night only; and regular customers/Saturday night only. The cost for each type of reservation is shown below. Two-Night Friday Night Saturday Night Package Only Only Convention $225 $123 $130 Regular $295 $146 $152 The anticipated demand for each type of reservation is as follows. Two-Night Package Friday Night Only Saturday Night Only Convention 40 20 15 Regular 20 30 25 Hanson Inn would like to determine how many rooms to make available for each type of reservation in order to maximize total revenue. (a) Formulate a linear programming model for this revenue management application. (Let CT = number of convention two-night rooms, CF = number of convention Friday only rooms, CS = number of convention Saturday only rooms, RT = number of regular two-night rooms, RF = number of regular Friday only rooms, RS = number of regular Saturday only rooms.) Max × s.t. anticipated demand for convention two-night rooms x anticipated demand for convention Friday night only rooms anticipated demand for convention Saturday night only rooms anticipated demand for regular two-night rooms anticipated demand for regular Friday night only rooms anticipated demand for regular Saturday night only rooms Friday night rooms available for convention attendees only Saturday night rooms available for convention attendees only Enter inequalities using less than (<), greater than (>), less than or equal (s), or greater than or equal (≥). Enter inequalities using less than (<), greater than (>), less than or equal (s), or greater than or equal (≥). Enter inequalities using less than (<), greater than (>), less than or equal (s), or greater than or equal (≥). × Enter inequalities using less than (<), greater than (>), less than or equal(s), or greater than or equal (≥). Enter inequalities using less than (<), greater than (>), less than or equal (s), or greater than or equal (≥). × Enter inequalities using less than (<), greater than (>), less than or equal (s), or greater than or equal (≥). Check which variable(s) should be in your answer. Check which variable(s) should be in your answer. total rooms available for Friday night Check which variable(s) should be in your answer. total rooms available for Saturday night Check which variable(s) should be in your answer. CT, CF, CS, RT, RF, RS ≥ 0 (b) What is the optimal allocation? CT x x × RT 20 RF 28 RS = From this allocation, what is the anticipated total revenue (in dollars)? ૐ

A linear programming computer package is needed. Hanson 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, Hanson increases its normal room rates and takes reservations based on a revenue management system. A large profesional organization has 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-night package, some attendees may select a Friday night only 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/two-night package; regular customers/Friday night only; and regular customers/Saturday night only. The cost for each type of reservation is shown below. Two-Night Friday Night Saturday Night Package Only Only Convention $225 $123 $130 Regular $295 $146 $152 The anticipated demand for each type of reservation is as follows. Two-Night Package Friday Night Only Saturday Night Only Convention 40 20 15 Regular 20 30 25 Hanson Inn would like to determine how many rooms to make available for each type of reservation in order to maximize total revenue. (a) Formulate a linear programming model for this revenue management application. (Let CT = number of convention two-night rooms, CF = number of convention Friday only rooms, CS = number of convention Saturday only rooms, RT = number of regular two-night rooms, RF = number of regular Friday only rooms, RS = number of regular Saturday only rooms.) Max × s.t. anticipated demand for convention two-night rooms x anticipated demand for convention Friday night only rooms anticipated demand for convention Saturday night only rooms anticipated demand for regular two-night rooms anticipated demand for regular Friday night only rooms anticipated demand for regular Saturday night only rooms Friday night rooms available for convention attendees only Saturday night rooms available for convention attendees only Enter inequalities using less than (<), greater than (>), less than or equal (s), or greater than or equal (≥). Enter inequalities using less than (<), greater than (>), less than or equal (s), or greater than or equal (≥). Enter inequalities using less than (<), greater than (>), less than or equal (s), or greater than or equal (≥). × Enter inequalities using less than (<), greater than (>), less than or equal(s), or greater than or equal (≥). Enter inequalities using less than (<), greater than (>), less than or equal (s), or greater than or equal (≥). × Enter inequalities using less than (<), greater than (>), less than or equal (s), or greater than or equal (≥). Check which variable(s) should be in your answer. Check which variable(s) should be in your answer. total rooms available for Friday night Check which variable(s) should be in your answer. total rooms available for Saturday night Check which variable(s) should be in your answer. CT, CF, CS, RT, RF, RS ≥ 0 (b) What is the optimal allocation? CT x x × RT 20 RF 28 RS = From this allocation, what is the anticipated total revenue (in dollars)? ૐ

College Algebra (MindTap Course List)

12th Edition

ISBN:9781305652231

Author:R. David Gustafson, Jeff Hughes

Publisher:R. David Gustafson, Jeff Hughes

Chapter6: Linear Systems

Section6.8: Linear Programming

Problem 5SC: If during the following year it is predicted that each comedy skit will generate 30 thousand and...

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