1. How long does it take to fill a rush order [from mix and spoon, Load oven, bake, cool pack, and receive payment] ? (For orders of one dozen, and for orders of two dozens-same ingredients.)
Answer: (a) for orders of one dozen __________ minutes According to the specified work arrangements, a Gant Chart (Basic case 1) is developed as follow:
As obviously indicated from the above chart, it takes 26 minutes to fill a one dozen rush order.
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DSME2030A ASSIGNMENT 1 (b) for orders of two dozens __________ minutes Assuming the work arrangement has not been adjusted, a Gant Chart (Basic case 2) for two dozens orders is developed as follow.
Therefore, it takes 36 minutes to finish a two dozens rush order. 2. For orders of one dozen, how many orders can you fill in a night? Assuming 4 hours
per night Answer: We can find from basic case 1 that we will spend 10 more minutes with one more dozen ordered, because the oven has already been fully utilized and become bottleneck under this circumstance. We know that the roommate can prepare oven for baking the second dozen just after finishing baking the first dozen, during the 10 minutes when the oven is prepared and the second dozen is baking, the first dozen can be cooled and packed in 7 minutes, and the remaining 3 minutes are enough for collecting money, moreover washing, mixing and spoon for the second dozen can be finished during the time of first baking. So we have proved that we need 10 more minutes when one more order are required. We can construct a formula to express relationship between time (T, in minutes) and number of dozen(X) T=16+10X Assuming 4 hours(240 minutes) per night, here is the formula 240 16 10 x x 22 So we can make 22 dozen of cookies and also 22 orders per night. Page 4 of 10
DSME2030A ASSIGNMENT 1 3.1 Given Kristen’s Cookie wants to maximize the profit, do you need to employ your roommate if all orders are one-dozen orders(assuming orders do not have the same ingredient)? Answer: If Kristen does not employ his roommate, he needs to spend 13 more minutes for each extra one-dozen order, that is, it will take him 13+13n minutes to finish n orders. (As the following Gant Chart illustrates). Assuming 4 hours per night, Kristen can get 17 orders` profit.
If Kristen employs his roommate, they need to spend 10more minutes for each extra one-dozen order (shown in basic case 1), that is, it will take them 16+10n minutes to finish n orders. (as discussed in question 2). Assuming 4 hours per night, they can get 22 orders` profit. We assume Kristen and his roommate share the profits based on their work time (excluding idle time), for each one-dozen order, Kristen spends 8 minutes and his roommate spends 4 minutes. So Kristen will share 1/3 profits with his roommate and keep 2/3 profits for himself. Thus, Kristen can get 44/3(about 14.67) orders` profit, which is less than 17 orders’ profit. From the comparison above, we can conclude: To maximize Kristen`s personal profit, Kristen does not need to employ his roommate if orders are one-dozen orders. To maximize Kristen Cookies` total profit, Kristen needs to employ his roommate if orders are one dozen orders.
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DSME2030A ASSIGNMENT 1 3.2 What if orders are two-dozen orders (assuming each two-dozen order has the same ingredients)? You may reassign the job for you and your roommate. Answer: Firstly, we can compare the following two situations With Roommate (the same as basic case 2 without work rearrangement)
Without Roommate (with rearrangement of work and 3 trays)
As the oven is fully utilized and become the bottleneck, we can see that Kristen doesn’t need to employ roommate if one more tray is used. Usually the cost of a tray would be cheaper than labor cost, so there is no need to employ roommate if the orders are two dozens.
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DSME2030A ASSIGNMENT 1 3.3 If orders are one-dozens orders, how many electric mixers...