The Production Process

Baking cookies is simple: place all the ingredients in a mixing bowl and mix them; spoon the cookie dough onto a tray; put the cookies into the oven; bake them; take the tray of cookies out of the oven; let the cookies cool; and, finally, take the cookies off the tray and carefully pack them in a box. You and your roommate already own all the necessary capital equipment: a high$-$capacity professional$-$grade electric mixer, cookie trays, and spoons. Your apartment has a small oven that will hold one tray at a time. Your landlord pays for all the electricity. The variable costs, therefore, are merely the cost of the ingredients $($estimated to be $$0\mathrm{.}60/$dozen$),$ the cost of the box in which the cookies are packed $($$$0\mathrm{.}10$ per box; each box holds a dozen cookies$),$ and your time $($what value do place on your time?$).$A detailed examination of the production process, which specifies how long each of the steps will take, follows. The first step is to take an order, which will be extremely fast and $100\%$ accurate, since your roommate has devised a method using the campus e$-$mail system to accept orders and to inform customers when their orders will be ready for pickup. Because this runs automatically on your personal computer, it does not take any of your or your roommate's time. Therefore, this step will be ignored in further analysis.You and your roommate have timed the necessary physical operations. The first physical production step is to wash out the electric mixer's bowl and beaters from the previous batch, add the ingredients to the bowl, and turn on the mixer to mix the ingredients. The electric mixer can hold and mix ingredients for up to three dozen cookies. You then spoon the cookies, one dozen at a time, onto a cookie tray. These activities take $6$ minutes for the washing and mixing steps, regardless of how many cookies are being made in the batch.That is$,$ to mix enough dough and ingredients forthree dozen cookies takes the same $6$ minutes as for one dozen cookies. However, spooning the cookies onto the tray takes $2$ minutes per tray.The next step, performed by your roommate, is to put the cookies in the oven and set the thermostat and timer, which in total takes about $1$ minute. The cookies bake for the next $9$ minutes. So total baking time is $10$ minutes, during the first minute of which your roommate is busy setting the oven. Because the oven only holds one tray, a second dozen takes an additional $10$ minutes to bake.Your roommate also performs the last steps of the process by first removing the cookies from the putting them aside to cool for $5$ minutes, then carefully packing them in a box andaccepting payment. Removing the cookies from the oven takes a negligible amount of time, but it must be done promptly. It takes $2$ minutes to pack each dozen and about $1$ minute to accept payment for the order.This is the process you plan to use to produce cookies by the dozen at Kristen's Cookie Company. As experienced bakers know, a few simplifications were made in describing the actual cookie production process. For example, the first batch of cookies for the night requires preheating the oven. However, such complexities will be put aside for now. Begin your analysis by developing a process flow diagram of the cookie$-$making process.

$1.$ How long will it take you to fill a rush order of two dozen cookies, assuming no other cookies are currently in process?

$2.$ Consider the current process. How many electric mixers and baking trays will you need?

$3.$ Suppose you use a second oven. What would be the capacity of the process?

$4.$ Suppose you use two ovens now. In addition, if you premix in advance and refrigerate doughs, the mixing step can be eliminated. What would be the capacity of the process?