a) For an upcoming red carpet evening, a company is selling tickets at $60 per person at a large theatre which has a capacity of 10,000 people. Each attendant is expected to buy $12 of food and merchandise at the film evening. The cost of providing the food and merchandise is estimated to be $5 per person. All other ancillary services will be provided by the theatre. Initial analysis indicates that the ancillary cost of providing food and merchandise, as well as the staff needed to handle ticket sales, may be described as a semi-variable cost. Data on these costs and tickets sold from three similar events held at the venue have been collected and are tabulated below:

Tickets Sold	Cost ($)
2100	6640
3824	11284
4650	13525

Use the high-low method to estimate the total cost function relating to these ancillary costs. b) The company will be renting the theatre which will host the upcoming red carpet evening. The budgeted fixed cost of both renting the theatre and paying the staff is budgeted to total $8,000. In addition, a TV entertainment channel will be paying the company $10,000 for the right to record and sell DVDs of the evening's highlights. Calculate the number of tickets needed to be sold for the company to earn an expected $90,000 profit from the comedy evening. c) The company is also organising a large all-day awards show with three different types of ticket: 'Adult', 'Child' and 'Family'. These different ticket types are sold at different prices, and allow ticket holders different seating options and entitlements (e.g. in-seat commentary, Wi-Fi access). The prices and variable costs associated with each ticket type are given below:

Ticket type	Selling Price ($)	Variable Cost ($)
Adult	80	50
Child	30	20
Family	190	170

Past experience has indicated that the mix of tickets sold for similar events has been 70% (Adult), 20% (Child) and 10% (Family). The company will be hiring an expo centre with a huge hall to accommodate a total capacity of 100,000 people. The company will be charged a fixed cost totalling $1.8m for use of the facilities. No other costs are anticipated by the management of the company. Calculate the number of tickets of each type that will allow them to break even on their planned Awards Show.