QuestionI: The Choice Resort $($CR$),$ 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 following information is available regarding the period of the tournament

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$)$ $$300000$

$2$ Accommodation for guests is provided on an all$-$inclusive basis $($meals$,$ drinks, entertainment etc$).$

$3$ The objective of the hotel management is to maximize profit.

$4$ 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$)($i$)$ Calculate the profit$-$maximizing fee per double room that MR 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.How to solve