dustial Managerment uestion A2 erseyRestaurant provides three takeaway dishes. A
ID: 339277 • Letter: D
Question
dustial Managerment uestion A2 erseyRestaurant provides three takeaway dishes. All these dishes are made using 3 types of cookware: ollowing number minutes oven, pan and heat oven. To prepare each dish, each cookware will need to be used for Cookware Dish 1 5 minutes 11 minutes 20 minutes Dish 3 12 minutes Dish 2 10 minutes 0 minute 17 minutes Pan Oven 13 minutes Each cookware has a limited numbor of available minutes, as shown in the following table: Available time (minutes 600 300 Pan Oven The unit profit would be E9, £5 and £12, for each unit of dish 1, dish 2 and dish 3, respectively The objective of the restaurant is to find the optimal number of units of each type of dishes to maximise profit You are required to provide a mathematical formulation for this problem Note: You need to show the detailed steps to create your formulation, including explanations on: The table of input parameters What are the decision variables, and their meaning What is the objective function, and it's meaning What are the constraints, and their meaning [15 marks] Spring 2017 Page 4 of 10Explanation / Answer
Assuming that quantities X1, X2 and X3 of dishes 1,2 and 3 are prepared respectively. These are decision variables.
The objectie function is to maximize the profit. i.e.
Max 9X1+5X2+12X3
Such that
5X1+10X2+12X3 <= 500
11X1+0X2+21X3 <=600
20X1+17X2+13X3 <= 300
X1, X2 and X3 =>0
The 4 equations listed above are constraints. For example, the eqaution 1 shows the time taken by three types of dishes manufactured in the Microwave. Since the maximum time a microwave can work is 500 min. the sum of the individul time values of three types of dishes should not be more than 500.
Same is true for the dishes to be manufactured with help of pan and oven.
Since there can be no negative quantity, X1, X2 and X3 need to be positive. These are non negativity constraints.
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