Problem:

You have been asked to provide a system for making fresh brownies for a church youth group fund-raiser. Since you are known to be a student at UST (and therefore are considered sharp as a tack), the Youth Council has asked you to plan the brownie project. Specifically, the Youth Council needs to know the cost per dozen of the brownies; the equipment needed; the number of people to schedule to help and the jobs that each of the volunteers will do; and how many dozen brownies can be made between 8:00 am and 3:00 pm Saturday morning. The list of volunteers, so far, has 12 people on it, and they all are familiar with making brownies and using the church kitchen. You know that there are some people on the list that would help if you asked them, but they would rather not if you have enough volunteers. Since some of the younger youth are available to carry raw materials, transfer pans, deliver brownies, etc., you are only concerned with the processes of mixing ingredients, transferring the ingredients to pans, cooking, cooling, cutting, and packing (1/2 dozen per box). The ovens will be preheated and bowls, spoons, etc. will be pre-positioned by 8:00.

You estimate that mixing will take 10 minutes per bowl. Each bowl can hold enough ingredients for 2 dozen brownies, and the church has 4 bowls. Transferring should take about 1 minute per pan, and each pan holds 1 dozen brownies. The church has 6 pans. You have 2 ovens available, each will hold 2 pans. The brownies should take about 12 minutes per pan to bake, and about 7 minutes per pan to cool. Slicing each pan into a dozen brownies takes about 2 minutes, and packing takes about 2 minutes per box. The costs of the ingredients is estimated to be $.75 per dozen; each box costs $.15.

Past experience has shown that the neighborhood community has a humongous sweet tooth, and will buy all of the brownies you can make, so your primary concern is to maximize the number of brownies you can make during the time available. You also know that the experienced volunteers are happy to help, but they need to be organized for the best output. As you think over this project during the week before "Brownie Day", you wonder about the different tasks to be performed, and how people should be assigned to the tasks.

Required:

Question 1) How many dozen may be made between 8:00 am and 3:00 pm if only the available equipment is used?

Question 2) What are potential "hot spots" or problems with this process? What are potential solutions?

Question 3) If you could add any equipment (except more ovens), what would you add? How would any additions affect the number of brownies produced?

Solve the problem and show all work.