The Raymond Co. is concerned that new gaming legislation will be passed whereby spending limits will be placed on gamblers. If this is the case, the company may restructure their business by reducing the number of poker machines and transforming a large part of the current gaming machine area into a venue where conferences can be held. This area will have 10 rooms with 3 levels of conferences experiences offered - deluxe, standard and basic which will be aimed specifically at corporate, community groups and clients. The rooms would be charged out at a daily rate. 

You are proposing that the deluxe service will see a conference room equipped with the latest technology including a café style coffee machine and the provision of all food (max of 20 people per room). The next service level is standard whereby morning and afternoon tea is provided with the option for attendees to eat at the restaurant (max. of 35 people per room). Lastly, the basic level of service offers only tea and coffee (max of 75 people per room).

The rooms are all the same size and the cost to clean each room is the same but depending on the type of service chosen by a client, other costs will differ. An estimated cost for a room according to each service type (deluxe, standard and basic) appears below with the budgeted cost limit.

Due to limits on the number of guests who may have access to the building at any one time, a maximum of one room offering basic service can be utilised per day and a minimum of two rooms offering deluxe services.

Required:

a) Formulate a linear program to determine the expected mix of conference rooms to ensure the maximum profit for Raymond Co. Show all supporting calculations and derive the optimum solution using a computer package.

b) Comment on the solution, was it what you expected? Why or why not?