Question $4$

$[23$ Marks$]$

Wembley Travel Agency specialises in flights between Johannesburg and Cape Town. It books passengers on South African Airways at R$3000$ per round$-$trip ticket. Until last month, South African Airways paid Wembley a commission of $10\%$ of the ticket price paid by each passenger. This commission was Wembley's only source of revenue. Wembley's fixed costs are R$15000$ per month $($for salaries, rent, etc.$),$ and its variable costs are R$100$ per ticket purchased for a passenger. This R$100$ includes a R$75$ per ticket delivery fee paid to Federal Express. Assume that each round$-$trip ticket purchased is delivered in a separate package. Thus, the R$75$ delivery fee applies to each ticket.

South African Airways has just announced a revised payment schedule for all travel agents. It will now pay travel agents a $10\%$ commission per ticket up to a maximum of R$160.$ Any ticket costing more than R$1600$ generates only a R$160$ commission, regardless of the ticket price.

Required:

Under the old $10\%$ commission structure, how many round$-$trip tickets must Wembley sell each month to break even $($a$),$ and to earn an operating income of R$7500$

$($b$)?$

$(11$ marks$)$

How does South African Airway's revised payment schedule affect your answers to

$($a$)$ and $($b$)$ in requirement $1?$

$(12$ marks$)$

Show all your workings.