Question: QUESTION 4- Simulation 125 marks Vic Books cafe on the ground floor of Rutherford House has been …

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Jun 13, 2022

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Question: QUESTION 4- Simulation 125 marks Vic Books cafe on the ground floor of Rutherford House has been …

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QUESTION 4- Simulation 125 marks Vic Books cafe on the ground floor of Rutherford House has been running for 8 months very successfully. However there are often long waits for coffees. Customers tend to amive bunches (for example between classes) and they are often in a rush for their coffee, so its important to keep wait times to a minimum, as far as possible. The manager of the cafè has heard that you have been studying business management and has asked for your advice. The process starts with the customer placing their order at the till. The cashier writes the order on a chit and attaches this chit to a sticky strip along the top of the coffee machine which is operated by a barista. The barista makes the drinks according to the order of the chits attached to the coffee machine. Drinks take different times to produce: for example a simple espresso is quick to make but a mocha made from coffee and heated chocolate-flavoured milk, plus a dusting of chocolate on top, plus a marshmallow, takes longer to prepare. The large takeaway cups generally take longer as there is more milk to heat, while have here coffees get a fancy decoration on top, but these tend to balance out and any small differences will be ignored for now. The ratio of drink types varies through the day, but on average about 10% choose espresso, 60% choose flat white (or similar), and 30% choose mocha. For simplicity, we will assume that an expresso takes 1 minute, while a mocha takes 3 minutes. Other drinks like a flat white or hot chocolate take 2 minutes. Customers can often arrive together and are sometimes spread out. The typical distribution of inter-arrivals times is provided in Table 1. o- Table 1: Distribution of inter-arrival times Inter-arrival time Probability minutes) .1 .2 .3 .35 .05 The Vic Books manager is interested to see the average wait time as well as the longest wait. a. Conduct a small simulation (up to 20 customers) using the information provided above and the random numbers supplied (please start in the middle column) to show how you could ascertain the average and longest wait times for a sample of customers. (15 marks) b. Comment briefly on your results noting any patterns and whether they are to be expected Indicate any limitations of such an analysis. (2 marks)
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QUESTION 4- Simulation 125 marks Vic Books cafe on the ground floor of Rutherford House has been running for 8 months very successfully. However there are often long waits for coffees. Customers tend to amive bunches (for example between classes) and they are often in a rush for their coffee, so it's important to keep wait times to a minimum, as far as possible. The manager of the cafè has heard that you have been studying business management and has asked for your advice. The process starts with the customer placing their order at the till. The cashier writes the order on a chit and attaches this chit to a sticky strip along the top of the coffee machine which is operated by a barista. The barista makes the drinks according to the order of the chits attached to the coffee machine. Drinks take different times to produce: for example a simple espresso is quick to make but a mocha made from coffee and heated chocolate-flavoured milk, plus a dusting of chocolate on top, plus a marshmallow, takes longer to prepare. The large takeaway cups generally take longer as there is more milk to heat, while 'have here' coffees get a fancy decoration on top, but these tend to balance out and any small differences will be ignored for now. The ratio of drink types varies through the day, but on average about 10% choose espresso, 60% choose flat white (or similar), and 30% choose mocha. For simplicity, we will assume that an expresso takes 1 minute, while a mocha takes 3 minutes. Other drinks like a flat white or hot chocolate take 2 minutes. Customers can often arrive together and are sometimes spread out. The typical distribution of inter-arrivals times is provided in Table 1. o- Table 1: Distribution of inter-arrival times Inter-arrival time Probability minutes) .1 .2 .3 .35 .05 The Vic Books manager is interested to see the average wait time as well as the longest wait. a. Conduct a small simulation (up to 20 customers) using the information provided above and the random numbers supplied (please start in the middle column) to show how you could ascertain the average and longest wait times for a sample of customers. (15 marks) b. Comment briefly on your results noting any patterns and whether they are to be expected Indicate any limitations of such an analysis. (2 marks)

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