# Profit Analysis for Small, Medium, and Large Operations Hubs

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BSc (Hons) Digital and TechnologySolutionsMaths for ComputingCoursework Assessment BriefWinter Term 2016
Maths for Computing2016 Coursework Assessment Brief1. Problem DescriptionBPP Lyft is a UK rival of Uber, the American multinational online transportation network companyoffering driver services to customers through its mobile app. They have been operating within the UKsuccessfully for many years, and despite the uncertainty surrounding Britain’s exit from Europe, theyare taking a long term view and are now considering further expansion of their fleet of autonomous‘self-driven’ vehicles by launching its services in Leicester. The managing director, Robert Jules (RJ),financial director, Eva Watkins (EW) and marketing director, Jonathan Kent (JK) have met recently todiscuss the decision. Below is an extract from that meeting which took place at the company’s mainheadquarters in London.RJ: We've finally been able to identify a suitable site for the new fleet in Leicester. The site has plentyofroom and we shall need to decide how large an operations hub to build. If we use one of our standarddesigns then we shall have to decide between a small, medium or large operations hub.Fixed & Variable CostsEW: The fixed costs clearly increase with size. We shall need to take into account the fixed costs pluscosts which are proportional to the actual sales revenue achieved. I've summarised the annual costsin this table:Fixed costsVariable costs(in £000's)(as a proportion of actual sales revenue)Small500.42Medium750.38Large1000.34Sales CapacityJK: But a larger hub gives us greater capacity. I think that if we just go for the smallest option we shallfind that we have not got the capacity for all the potential demand in Leicester and so miss out onpotential profit. Additionally, we are likely to be overrun by our main competitor Uber, who alreadyhave a strong presence in the city. The maximum annual sales that are possible from small, mediumand large scale operations are £200,000, £275,000 and £350,000 respectively.Revenue PotentialRJ: Well do we have any idea of the driver revenue that will be generated by the new location?JK: We've done some analysis based on our experience elsewhere and the likely competition, butthere's still a lot of uncertainty. The results can be summarised as a probability distribution of themarket share we get of the total driver revenue in the Leicester area.Market share0.050.060.070.080.090.10Probability0.10.10.30.20.20.1

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