Briz Guards is a Brisbane based company providing security services to mid-size organizations. Its primary clients are corporate offices, colleges and shopping malls. As of 2021, Briz Guards had 90 clients across the three sectors, with 20 clients in the colleges sector, 40 clients in the offices sector, and 30 clients in the malls sector. Briz Guard charges a uniform service fee of $200,000 per client, with a fixed cost of 500,000 per sector (see table below for a summary of this information).

SectorNo. of clientsService fee per clientFixed costs

College20$200,000$500,000Offices 40$200,000$500,000Malls30$200,000$500,000

Colleges 20 $200,000 Offices 40 $200,000 Malls 30 $200,000

$500,000 $500,000 $500,000

The company had been earning less than 10% returns for the past five years and is now embarking on a profitability analysis and expansion path with a stated objective of $3,000,000 in profits. It has identified two main strategies to increase its profits: acquiring new customers; and/or increasing the profitability of its existing customers. Briz Guards has hired you as its marketing consultant to analyse the profit potential of different strategies and advise them on which one to pursue. Briz Guards has provided following information about its clients to enable your analysis.

The company applies a discount rate of 10%.

Retention rate for all clients in all three sectors (offices, colleges, malls) is 95%.

The dataset gives the average annual expenses per client across the three sectors.

The company has to invest $100,000 for prospecting a new client

The companys prospecting has an acquisition rate of 15%.

In addition, its marketing department has provided you with its demand equations for each sector, based on its past pricing experience.

Colleges: No. of Clients (demand) = 100 - [(Service fee * 4) / 10,000]

Offices: No. of Clients = 100 - [(Service fee * 3) / 10,000]

Shopping Malls: No. of clients = 100 - [(Service fee * 3.5) / 10,000]

what are the formulas to find the data?

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