Management is currently exploring the option to expand service offerings to include weekend package options. Three weekend accommodation/meal packages are being considered. With average occupancy around 70% and the majority are corporate clients who stay during the week, it is believed the inclusion of package options will result in an overall increase in weekend sales for which there is capacity for increase.

The expected selling price and costs for the packages are as follows and reflect a differential in the quality of the product being provided from a basic package through to a luxury package.

	Package 1	Package 2	Package 3
Selling price	$200.00	$300.00	$450.00
Costs
Meal	30	60	100
Beveridge	20	40	70
Decoration	15	40	60
Accommodation	100	120	160

Under current staffing it has been determined that staff availability to perform the extra functions annually would be 40 hours for meals and 50 hours for beverages, 30 for decorations(table decorations, personalising welcome letter etc) and 50 hours for accommodation. The additional time to plan each of the package specifics, taking into account customer preferences, instruct purchase orders for each booking would be:

Constraints (minutes required)	Package 1	Package 2	Package 3
Meal	9	12	18
Beveridge	6	9	18
Decoration	6	12	15
Accommodation	6	6	12

Required:

a) Formulate a linear programming model to determine the mix of packages to offer to maximise profit, showing all supporting calculations, and solve using a computer package (eg solver in Excel) to derive an optimum staffing schedule. (15 marks)

b) Comment on the solution including recommending if the packages should be offered and under what conditions (if any). (10 marks