Practice Questions
PRACTICE QUESTIONS FOR NEWSVENDOR MODEL
1. Burger prince buys top-grade ground beef for $3 per kg. A large sign over the entrance guarantees that the meat is fresh daily. Any leftover meat is sold to the local high school cafeteria for $2 per kg. Eight hamburgers can be prepared from each kilogram of meat. Burgers sell for $2 each. Labour, overhead, meat, buns and condiments cost $1 per burger. Demand is normally distributed with a mean of 400 kg per day and a standard deviation of 50 kg per day. What daily order quantity is optimal? 2. A manager is going to purchase new processing equipment and must decide on the number of spare parts to order with the new equipment. The spares cost $200 each, and any unused spares will have an expected salvage value of $50 each. The probability of usage of parts can be described by the following distribution Number 0 Probability 0.1 1 0.5 2 0.25 3 0.15
If a part fails and a spare is not available, it will take two days to obtain a replacement and install it. The cost for idle equipment is $500 per day. What quantity of spares should be ordered? 3. The daily demand for muffins, at a campus cafeteria in McGill University, recorded to the nearest 10 muffins, has been recorded for 50 consecutive days with the following results: Number of Muffins 50 60 70 80 90 100 110 120 130 140 Number of Days 1 2 3 5 8 10 10 6 3 2
Each muffin costs $1.00 to bake and muffins sell for $2.25 each. Any muffins left over at the end of the day can be sold hungry students at $0.50 apiece. (a) Determine the number muffins to bake every day in order to maximize expected daily profit. (b) What is the expected daily profit when the optimal number of muffins is baked daily? (c) The mean and standard deviation of daily demand has been estimated to be 50 muffins and 10 muffins, respectively. Furthermore, it has been suggested that the distribution appears to be normal. (i) Determine the optimal number of muffins to bake daily. (ii)Specify the profit
1. Burger prince buys top-grade ground beef for $3 per kg. A large sign over the entrance guarantees that the meat is fresh daily. Any leftover meat is sold to the local high school cafeteria for $2 per kg. Eight hamburgers can be prepared from each kilogram of meat. Burgers sell for $2 each. Labour, overhead, meat, buns and condiments cost $1 per burger. Demand is normally distributed with a mean of 400 kg per day and a standard deviation of 50 kg per day. What daily order quantity is optimal? 2. A manager is going to purchase new processing equipment and must decide on the number of spare parts to order with the new equipment. The spares cost $200 each, and any unused spares will have an expected salvage value of $50 each. The probability of usage of parts can be described by the following distribution Number 0 Probability 0.1 1 0.5 2 0.25 3 0.15
If a part fails and a spare is not available, it will take two days to obtain a replacement and install it. The cost for idle equipment is $500 per day. What quantity of spares should be ordered? 3. The daily demand for muffins, at a campus cafeteria in McGill University, recorded to the nearest 10 muffins, has been recorded for 50 consecutive days with the following results: Number of Muffins 50 60 70 80 90 100 110 120 130 140 Number of Days 1 2 3 5 8 10 10 6 3 2
Each muffin costs $1.00 to bake and muffins sell for $2.25 each. Any muffins left over at the end of the day can be sold hungry students at $0.50 apiece. (a) Determine the number muffins to bake every day in order to maximize expected daily profit. (b) What is the expected daily profit when the optimal number of muffins is baked daily? (c) The mean and standard deviation of daily demand has been estimated to be 50 muffins and 10 muffins, respectively. Furthermore, it has been suggested that the distribution appears to be normal. (i) Determine the optimal number of muffins to bake daily. (ii)Specify the profit