Easy Carwash is a small local shop offering premium hand car washing services, including express wash and ultimate clean. Prevailing prices in the local market are $30 for an express wash, exterior only and $75 for an ultimate clean, both interior vacuuming and exterior cleaning.
For daily operation, The shop owns a cleaning crew of 10 people, 5 in charge of washing, 3 in charge of drying, and 2 in charge of vacuuming, all of whom work a typical 8-hour per day. The owners of the shop are looking for how to best organise the cleaning crew to maximise the prot to expand the business next year. Based on the previous experience, it is expected that an average of 30 minutes of washing time will be required for each express wash service. An ultimate clean service will require an average of 45 minutes washing time and 20 minutes vacuuming time. 25 minutes of drying time will also be required for each express wash or ultimate clean service.

Construct a mathematical model for this problem. In doing so, consider the following:
(a) What are the decision variables for this problem?
(b) Using decision variables identified in part (a), formulate the objective
function for this problem. Is the quantity of interest to be maximised or minimised?
(c) What constraints are relevant to this problem? Using the decision variables from part (a), formulate those constrain