Linear Programming – Leadership in Business

Alex Matteo is a former partner of a professional accounting firm who values education.         Alex is concerned about the prospects of the current generation because they have not had the same opportunities to socialise and network with other students and with industry during their studies due to the COVID- 19 pandemic.  Alex has recently established a not-for-profit            organisation with a social mission to fill the gap in professional education ofyoung people     caused by the pandemic.  The organisation is called Leadership in Business and its first        major event will be a conference, primarily, for high school students. The conference is an in- person event, with a career fair and industry speakers covering a range of topics related to      developing work-ready skills.  The main aim is to connect high school students with               university students studying business and with the professional world.

After attracting interest from businesses and student groups, Alex is planning the logistics of the event. The event will be held on a Saturday and Sunday from 10am to 5pm. The venue    will only allow 300 attendees per day. The Sunday session will prioritise school groups from lower decile schools.

Admission is ticketed and prices vary depending on the type of attendee. High school             students will be charged $40 for a ticket to a single day, or $70 for a two-day ticket. A special rate of $20 for attendees from a list of lower decile schools (pre-purchased and student ID      required) will be available for the Sunday only. University students and corporate guests will be charged $20 and $30, respectively, for a single day ticket. While they are not the main       targets, university students and corporate members would like to ‘give back’ to help high       school students and they also benefit from the chance to network.

Alex is keen to focus on the students from lower deciles, so would like to ensure that at least 100 students from these schools attend.  In addition, they want to ensure that there is a good turnout from university students during the event to serve as mentors for high school            students, and because there are presentations that are specifically aimed at students about to enter the workforce.  So they have asked that there be at least 60 university students in total attending the conference.

Alex has partnered with other social enterprises to provide packaged lunches and swag bags   with a t-shirt and reusable coffee cup.  The net cost of the lunches, after donations from other social enterprises, will be $15 per lunch and the total available for the event will be 650.  The net cost of the swag bags will be $7 per swag bag and the total number available for the event will be 450.  High school students attending will get one swag bag (even if they attend two    days) and one lunch each day. University and corporate guests will only get lunch.

Coffee and juice will also be available as part of the ticket price. High schoolers can have two juices per day. University students can get one coffee and one juice. Corporate guests can get two coffees. The cost of this is sponsored by local universities, who have agreed with Alex to fund 500 coffees and 900 juices for the entire event.

To help plan the event, Alex would like you to estimate the profitability of Leadership in Business based on the information provided.  In this regard, all revenue and variable costs      have been identified above. Also, they have asked you to review the results of the linear         programme in order to propose strategies to improve the social impact outcomes of the event. You decide that a linear programme would be useful for this.

Required

You are required to prepare a memorandum to Alex Matteo on the first event to be held by Leadership in Business. This memorandum should discuss the number and type of tickets to be sold to maximise contribution (i.e. total revenue less total variable costs).  Your advice     should reflect the fact that they are not familiar with linear programming:

a)  Formulate and solve a linear programme in Excel using the Solver function.

b)  Review the results of the linear programme to identify ways to improve capacity

utilisation and social impact outcomes.

•     Propose one area where further investment would help to improve the capacity

utilisation for the event. Refer to the linear programming results to justify your

selection and describe the potential impact.

•     Propose one way to further improve the social objective outcomes of the event. This

should refer to facts in the case where possible.

c)   Prepare a memorandum for Alex 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 ofyour linear programme from part (a) above. This should include

details of the maximum contribution 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 proposed in part (b) above.

•     An appendix containing the linear programme equation showing the objective

function and constraints, together with your variable definitions. This can be hand-

written or printed. (This should be in equation-form not the Excel version from part

(a))

•    An appendix containing the Excel Answer and Sensitivity Reports from part (a).

d)    Prepare a two-minute video that describes the main elements of your linear programme.

•     Briefly describe the goal and requirements in your linear programme and how they

are reflected in the spreadsheet.