Quantative Methods or business-Linear Programming

Case study – The Treetop Retreat

Since your previous quantitative analysis for George and Jane Forrester, owners of The Treetop Retreat, business has been good. The renovations of two of the treehouses are finished and these are proving to be popular choices for guests. George and Jane are well on the way to having enough funds to build their small café. The new laundry facilities have streamlined operations and provided additional benefits for guests.
With these physical improvements made, George and Jane are turning their attention to improving their marketing strategy. They were impressed with your previous report and have commissioned you to prepare another one on their new plans.
George and Jane realise that they need an internet presence. At their initial consultation with a website developer, it was suggested that they consider an online booking facility as all bookings are currently made via phone or through an agent. Before going ahead with this additional expense, George and Jane want to understand how likely it is to be used, particularly by the group of travellers most likely to stay at The Treetop Retreat.
Jane has found research suggesting that offering an incentive to guests who book well in advance of their planned stay will reduce variability of occupancy. Jane would like you to analyse the impact of introducing an incentive scheme.
Once the new website is set up, George and Jane want to undertake some local advertising for The Treetop Retreat. They have a limited budget but want to ensure that they reach a sufficient number of TV viewers, radio listeners and newspaper readers to make their campaign a success. They need your help to determine the best mix among the advertising media.
Perform the necessary quantitative analyses and prepare a business report for George and Jane Forrester, where you describe your findings and make appropriate recommendations. Specifically, perform the tasks outlined in this document and include FULL details of your working out in the Appendices. You will need to do the analysis and calculations that go in the appendices BEFORE you write your report. Read and understand this whole template before you begin.

George and Jane Forrester, owners.

Write a report-style discussion of the main results of your analysis in Appendix 1. You may use subsections, tables etc. as you see fit.

Currently bookings for The Treetop Retreat are made via phone or through a travel or tourism agent. George and Jane plan to update their internet website and are considering allowing guests to book online. They have come across a data summary from a recent survey that describes the method used by travellers to make their most recent holiday accommodation booking, broken down by age group.

Information obtained from another source suggests that members of Generation X are most likely to participate in nature-based activities (like staying at The Treetop Retreat), so George and Jane are interested in whether this booking method will appeal to those in this age group.

See the questions in Appendix 1 for detailed instructions on the analysis that is to be performed. In Appendix 1 there is a contingency table that summarises the methods used by 700 travellers to book their most recent holiday accommodation. Include the contingency table in your appendix, but not in your report.

Discussion in the report :
• Introduce the aim of this section of the report.
• Include your 100% stacked column chart in your report, and comment on any significant features.
• Report the answers to questions (b)-(e) from Appendix 1 but do not include the calculations.
• Specifically discuss any differences between the different age groups for the data shown in the contingency table.
• Use the results of the probability calculations and your observations from the column chart to make some recommendations about whether George and Jane should pursue the option of allowing guests to book online.
2. Offering an incentive for early bookings
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Write a report-style discussion of the main results of your analysis in Appendix 2. You may use subsections, tables etc. as you see fit.
Do not include numerical calculations. These should be placed in Appendix 2.
Do quote quantitative results.

Bookings for The Treetop Retreat are made anywhere from a couple of days to several weeks in advance. To reduce the uncertainty, George and Jane are considering offering an incentive (for example, a lower nightly tariff or a complementary breakfast) to guests who book well in advance of their stay. George and Jane want you to analyse the impact on the number of days in advance that bookings are made if an incentive is offered. Detailed instructions are in Appendix 2.

Discussion in the report:
• Introduce the aim of this section of the report including an explanation of the data to be analysed.
• Use Excel to produce a histogram for each set of booking data. Include the histograms in your report. Briefly describe for George and Jane what the histograms show. Include an explanation for the choice of bin size.
• Interpret the appropriate measures of central tendency and dispersion in non-statistical terms and compare these values for the data before and after the incentive was introduced (based on your analysis in Appendix 2). What effect did the introduction of the incentive have on the number of days in advance that bookings were made?
3. Advertising The Treetop Retreat

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Write a report-style discussion of the main results of your analysis in Appendix 3. You may use subsections, tables etc. as you see fit.
Do not include numerical calculations. These should be placed in Appendix 3.
Do quote quantitative results.
In the lead-up to summer, George and Jane have decided to embark on an advertising campaign through local media, specifically: community TV, newspaper ads, and two types of radio advertisements. To be effective, they think they should reach an audience of at least 175,000 people but would like the advertising campaign to cost as little as possible. The most George and Jane can afford to spend is $7500. George and Jane have some ideas on how they would like to spread their advertising among the four types of media.

See Appendix 3 for a detailed description of the problem. Model this optimisation problem as a linear program — instructions are in Appendix 3. Use the Solver in Excel to find an optimal solution.

Discussion in the report:
• Introduce the aim of this section of the report.
• Using mainly the Answer Report from Excel, describe the optimal solution. Your variable names will not appear here. Rather, you will make statements like: ‘To conduct an effective marketing campaign while minimising costs, The Treetop Retreat should purchase six minutes of TV advertising, …’.
• Comment on which constraints appear to determine the optimal solution (the binding constraints).
• For each constraint that is not binding, state and interpret the amount of slack.

Discuss the results of the other questions asked in Appendix 3.
• What is the effect on the optimal solution and on the overall cost of the advertising campaign if George and Jane are able to negotiate a lower price per minute of normal radio advertising?
• What action do you recommend George and Jane take if an additional newspaper ad block becomes available? Justify your answer.
• What is the effect on the optimal solution and on the overall cost of the advertising campaign if an audience of at least 200,000 is required?
• What is the optimal mix of advertising if the budget is limited to $6000? How many people will be reached by the

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