A hotel and conference center at a holiday destination can cater for a maximum of 540 tourists and conference attendees per month but does not open for business in any month in which the number of bookings is less than 300. The number of tourist bookings is always greater than or equal to the number of conference attendees but never more than twice as many. The profit made per tourist per month is $16 while the profit made per conference attendee per month is $19. What mix of conference attendees and tourists should the center aim for to maximize the profit and what is the maximum profit? Formulate an LP model for this problem and report the model in the box below. Your model must include clearly defined decision variables, an objective function, and the required constraints.

Question

Business

Gill

25 February, 14:42

A hotel and conference center at a holiday destination can cater for a maximum of 540 tourists and conference attendees per month but does not open for business in any month in which the number of bookings is less than 300. The number of tourist bookings is always greater than or equal to the number of conference attendees but never more than twice as many. The profit made per tourist per month is $16 while the profit made per conference attendee per month is $19. What mix of conference attendees and tourists should the center aim for to maximize the profit and what is the maximum profit? Formulate an LP model for this problem and report the model in the box below. Your model must include clearly defined decision variables, an objective function, and the required constraints.

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Answers (1)

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Maribel · Answer 1

Below is the solution. Feel free to ask any question in the comments.

Explanation:

Decision variables:

x = number of conference attendees, y = number of tourists, z = profit in $

Objective function:

Maximize z = 19x + 16y

Constraints:

x + y ≤ 540

x + y ≥ 300

x ≤ y, that is x - y ≤ 0

2x ≤ y, that is 2x - y ≤ 0

x ≥ 0, y ≥ 0