QMB求救

林子峰

1. How can AAT Airlines optimise in-flight meal serviceprofits?
(25 marks)

Preparing the in-flight meals for which AATAirlines is renowned involves producing meals in an airport kitchen by anexecutive chef, who insists on using only fresh ingredients.  Thetotal budget for food production for one flight is $240.  To keep food items tasting ‘kitchen fresh’, AAT Airlines ensures that the timetaken to make all food items does not exceed 6 hours before being delivered toa flight.  When on board, if a passengerrequests a food item that has sold out, AAT Airlines has a Meal ofChoice Reimbursement policy, which entitles the customer to adiscount off the purchase of that same item on a future flight.  The total budget allocated to thisreimbursement scheme is $225 per flight.  The table below contains the profits made fromthe sale of the food items to passengers, as well as other costs andrequirements on a single flight:

	Vegetarian	Beef Salad Roll	Croissant	Espresso
Profit per  meal type	$2.00	$2.00	$1.60	$1.50
Time Taken  to make Food Item (minutes)	2	1.5	1	1
Food Budget    (cost per item)	$2.00	$1.75	$0.75	$0.60
Meal of Choice Reimbursement	$1.50	$1.50	$1.00	$0.50

Shelf space on the trolley is limited to storing 210 food items on asingle flight, enough to cover the number of seats on board and crew members.  From recent analysis, it is also known that atleast 60 Vegetarian meals are sold on each flight.  AAT Airlines is interested in maximising theprofit from their food service and wish to know the optimal combination of fooditems to sell, to achieve this maximum.

Calculations for Original LinearProgram

a)      Formulatea linear programming model for AAT Airlines.  In doing so, clearly indicate the following:

·       What are the decisionvariables?  Define them precisely.

·       What is the objective?  Using your decision variables, formulate theobjective function.

·       What are the constraints?  Using your decision variables, formulate theseconstraints.

Include the full mathematical model in this section.

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