dec 2016 help hare

Hare Events is a company which specialises in organising sporting events in major cities across Teeland. It has approached the local council of Edglas, a large city in the north of Teeland, to request permission to host a running festival which will include both a full marathon and a half marathon race.

Based on the prices it charges for entry to similar events in other locations, Hare Events has decided on an entry fee of $55 for the full marathon and $30 for the half marathon. It expects that the maximum entries will be 20,000 for the full marathon and 14,000 for the half marathon.

Hare Events has done a full assessment of the likely costs involved. Each runner will receive a race pack on completion of the race which will include a medal, t-shirt, water and chocolate. Water stations will need to be available at every five kilometre (km) point along the race route, stocked with sufficient supplies of water, sports drinks and gels. These costs are considered to be variable as they depend on the number of race entries.

Hare Events will also incur the following fixed costs. It will need to pay a fixed fee to the Edglas council for permits, road closures and support from the local police and medical services. A full risk assessment needs to be undertaken for insurance purposes. A marketing campaign is planned via advertising on running websites, in fitness magazines and at other events Hare Events is organising in Teeland, and the company which Hare Events usually employs to do the race photography has been approached.

The details of these costs are shown below:
Full marathon
Half marathon
($)
($)
Race packs
15.80
10.80
Water stations
2.40
1.20

$
Council fees
300,000
Risk assessment and insurance
50,000
Marketing
30,000
Photography
5,000

Hare Events wishes to achieve a minimum total profit of $500,000 from the running festival.

What are the number of entries Hare Events will have to sell for each race in order to achieve this level of profit, assuming a constant sales mix based on the expected race entry numbers applies?

Work to the nearest whole number.

Full marathon: 17,915 entries and half marathon: 12,540 entries
Full marathon: 17,915 entries and half marathon: 12,540 entries

Full marathon: 14,562 entries and half marathon: 18,688 entries
Full marathon: 14,562 entries and half marathon: 18,688 entries

Full marathon: 20,000 entries and half marathon: 8,278 entries
Full marathon: 20,000 entries and half marathon: 8,278 entries

Full marathon: 9,500 entries and half marathon: 6,650 entries
Full marathon: 9,500 entries and half marathon: 6,650 entries