Brooke Young runs Young Yachting Pty Ltd. Brooke is a graduate of a tourism and hospitality degree and offers a luxury fully catered yachting holiday experience that includes scuba diving, swimming and being towed behind the yacht on a flotation device. Brooke charges her time to the venture at \($400\) per day and she organises the holidays and runs the yacht. She employs Woojin to cook and pays him \($350\) per day and employs Imogene to organise the scuba diving and other activities for \($320\) per day. Two families have approached Young Yachting Pty Ltd to take their families on a five day yachting holiday in the last week of January but Brooke can only run one yachting holiday at a time and has to choose which alternative will maximise profit. The Purkiss family has five people and they want the deluxe holiday while the Mellor family has six people but only want the standard holiday. The fixed costs of running the yacht for seven days are \($4200\), variable costs for the deluxe holiday are \($240\) per person per day including food and drinks and for the standard holiday are \($200\) per person per day. The deluxe holiday is priced at \($1200\) per person per day while the standard holiday is \($900\) per person per day.

Required

(a) Using only the differential income and expenses determine which family Brooke should take on the yacht in the last week of January.