Cooking With My Roommate’s

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The time cycle of my roommate is comprised of three tasks: setting the thermostat and time takes 1 minute, packing the cookies takes 2 minutes, and collecting payment takes 1 minute. In total, these tasks amount to 4 minutes (1 + 2 + 1 = 4 minutes). When both of our times are combined, it totals to 8 + 4, resulting in a total time of 12 minutes per order between the two of us. Since each baking tray can hold a dozen cookies exactly, we sell cookies by the dozen. If customers order two dozen cookies, three dozen cookies, or more, should a discount be offered?

Ordering multiple dozens of cookies does not significantly increase the time it takes to fill the order compared to a one-dozen cookie order. In fact, producing the second and third dozen of cookies only takes slightly less time. To account for this slight difference, we offer a discount of 10-20% off if you order a second or third dozen. As we discovered in the previous problem, it takes 12 minutes (6+2+1+2+1) to produce one dozen cookies. Producing two dozen cookies takes 17 minutes (6+2+1+2*2+1), while producing three dozen takes 22 minutes (6+2+1+2+1).

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Regarding the ingredients and boxes, if we sell more dozens to a customer rather than just one, we can save time and still be profitable by offering a discount. So, how many electric mixers and baking trays will you need? We would suggest using one electric mixer since it remains idle for a long duration during production. As for baking trays, we would require three because a single mixer cannot handle more than three dozens of ingredients throughout the entire process. Additionally, are there any changes you can make in your production plans to enhance the quality, quantity, time efficiency, or cost-effectiveness of your cookies? Firstly, creating a cookie menu would expedite customer orders and processing times. Secondly, freezing pre-made cookie dough balls would significantly reduce processing time by simply retrieving the frozen balls from the freezer when an order is placed. Lastly, incorporating a second oven could further improve the process.

By adding a second oven, we can increase the output of cookies, assuming there is enough demand for them. The current bottleneck in the process is mixing the ingredients and spooning them onto a tray. If we include another oven, the production rate can be increased to 7.5 dozen per hour, compared to the previous rate of 6 dozen per hour with one oven. As a result, the nightly capacity of the process will increase from 24 to 30 dozen per night. In other words, the addition of another oven will lead to a nightly increase of 6 dozen cookies. However, it is only worth considering if there is sufficient demand and we are able to fulfill orders.

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