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Learning objectives
• Demonstrate proficiency in linear programming and Excel within a contextual setting
• Develop and apply strategies to refine the estimates used in linear programming
• Exercise professional skill in writing reports
Linear Programming – Cooper’s Retreat
You have offered to help organise Cooper’s Retreat, an event designed to bring students and
corporate workers together in a casual environment to unwind after a busy work day, as well
as an opportunity to mingle and network. Hugh Cooper, the organiser of this event, is an
internationally renowned business speaker who is planning to tour New Zealand universities.
The Auckland event is the first and will be held on a Friday evening during the University of
Auckland’s mid-semester break. Cooper’s Retreat will feature live music from local bands
and bar service to be held in a ‘pop-up’ marquee that will be set-up in an otherwise unused
space around the campus. As an unlicensed event, they plan to offer complimentary freshly
squeezed juice and premium soft-drinks.
After attracting interest from businesses and student groups, Hugh is planning the logistics of
the event. The event will be held from 4pm to 10pm. The marquee and location will only
allow 250 attendees.
Admission is ticketed and attendees buy tickets for three-hour time sessions. The afternoon
session is from 4pm to 7pm and the evening session from 7pm to 10pm. Students will be
charged $22 for a ticket to a single session, or $40 for a ticket to both sessions. Corporate
guests will be charged $29 for a ticket to a single session, or $50 for a ticket to both sessions.
When asked about expected numbers of attendees, Hugh replies:
“Err… I’m really not that sure. It’s the first event. So it could be quiet. There has
been a good response from companies and I think it’d be a cheap time out for
students. It being a Friday would also help… let’s just say 80 people for each
ticket type and we can play around with that figure later.”
Discussing the event further with Hugh you estimate that, over the course of three hours, a
student will have three soft drinks and one juice, while a corporate guest will have one soft
drink and two juices. Kitchen space is limited. There will only be enough refrigerator space
for 800 soft drinks for the whole event. The juicing area is also a concern as staff will need to
prepare fruit and vegetables, juice them to order, and serve customers. You expect to be able
to provide 350 servings of juice in the afternoon session as staff can prepare servings ahead
of time. This estimate will decrease to 250 servings for the evening session when staff have
to prepare juice during the evening. The cost of providing each soft drink is $2, and $3 for
each juice.
During his initial talks with businesses and student groups about the event, Hugh is
approached by Trajectory, a local business organisation, who would like to run a competition
in the month leading up to the event. For each day in August, Trajectory are looking to offer
a prize for one full event corporate pass (a corporate ticket to both afternoon and evening
sessions). Hugh views this as good advertising for the event and the necessary tickets will be
presold, and Trajectory will pay the full price for these tickets.
To help plan the event, Hugh would like you to estimate the profitability of Cooper’s Retreat
based on the information provided. Further, Hugh has also asked you to investigate the likely
demand for the event by ticket type, and examine the effect this is likely to have on the
event’s profitability. You decide that a linear programme would be useful for this.
Required
You are required to prepare a memo to Hugh Cooper on Cooper’s Retreat that discusses the
tickets to be sold to maximise their profit. Your advice should reflect the fact that Hugh is
not familiar with linear programming:
a) Formulate and solve the linear programme in Excel using the Solver function. Attach as
appendices to your memo copies of your:
• Linear programme equation showing the objective function and constraints, together
with your variable definitions. This can be hand-written or printed.
• Excel spreadsheet containing the linear programme.
• Excel Answer Report and Sensitivity Report.
b) Develop and apply strategies to refine the demand estimates provided by Hugh. You
anticipate there would be a maximum demand of 100 for any given ticket (representing
“peak” demand), with a minimum demand of 30 for any ticket (“quiet” demand).
• Develop two strategies you would use to investigate and refine the demand estimates
for the event. Your strategies may use experiential or empirical approaches.
• Apply at least one of the strategies you described to refine the demand estimates.
Re-solve the linear programme under these different conditions to explore how
changes in demand will affect the profitability of the event.
c) Prepare a memo for Cooper’s Retreat that discusses the following areas:
• A brief overview of your linear programme and its role in solving the business
problem. This should include a description of the linear programme’s objectives as
well as the role of explicit and implicit constraints.
• The results of your linear programme in Part A. This should include details of the
maximum revenue that could be earned, what the final values represent, which
constraints are binding, and what the shadow prices mean.
• An overview of the strategies you employed in Part B to refine the demand estimates
for the LP. For each strategy, describe the methods to be used, data sources, and the
likely accuracy of the results. Briefly discuss the insights from the results you
observe when re-solving the linear programme.
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