The Choice Resort $($CK$),$ which is privately owned, is a world famous luxury hotel and golf complex. It has been chosen as the venue to stage "The Robyn Cup', a golf tournament which is contested by teams of golfers from across the globe, which is scheduled to take place during July $2009.$ CR will offer accommodation for each of the five nights on which guests would require accommodation.The followinginformation is available regarding the period of the tournament$1.$ Hotel data:Total rooms $2400$ Room mix:Double rooms $75\%$Single rooms $15\%$Family rooms $10\%$Fee per room per night $($$$)$:Double rooms $400$Single rooms $300$Family rooms $600$Number of guests per room:Double rooms $2$Single rooms $1$Family rooms $4$When occupied, all rooms will contain the number of guests as above.Costs:Variable cost per guest per night $$100$Attributable fixed costs for the five$-$day period:Double rooms $$516000$Single and family rooms $($total$)$ $$3000002$ Accommodation for guests is provided on an all$-$inclusive basis $($meals$,$ drinks, entertainment etc$)\mathrm{.}3$ The objective of the hotel management is to maximize profit$\mathrm{.}4$ The hotel management expect all single and family rooms to be $\text{'}$ sold out' for each of the five nights of the tournament.However, they are unsure whether the fee in respect of double rooms should be increased or decreased. At a price of $$400$ per room per night they expect an occupancy rate of $80\%$ of available double rooms. For each $$10$ increase$/$ decrease they expect the number of rooms to decrease$/$ increase by $40.$Required:$($a$)(1)$ Calculate the profit$-$maximizing fee per double room thatMR should charge per night during the Tournament. $($ii$)$ Calculate how much profit would be earned from staging the tournament as a consequence of charging that fee.$($b$)$ The management of the hotel are concerned by the level of variable costs per guest night to be incurred in respect of the tournament, A recent review of proposed operational activities has concluded that variable cost per guest per night in all rooms in the hotel would be reduced by $20\%$ if proposed changes in operational activities were made. However, this would result in additional attributable fixed costs amounting to $$200000$ in respect of the five day period.Advise management whether, on purely financial grounds, they should make the proposed changes in operational activities.