I'm totally lost here!!
Your team has been called in to solve a problem encountered by a fast food restaurant. They believe that their coffee should be brewed at 170 deg Fahrenheit. However, at temperature it is too hot to drink, and a customer who accidentally spills the coffee on himself might receive third degree burns.
What they need is a special container that will heat the water to 170 deg, brew the coffee at that temperature, then cool it quickly to a drinkable temperature, say 140 deg F and hold it there, or at least keep it at or above 120 deg F for a reasonable period of time without further cooking. Yo cool down the coffee, 3 companies have submitted proposals with these specifications.
a)the Centikeeper Company has a container that will reduce the temperature of a liquid from 200 deg F to 100 deg F in 90mins by maintaining a constant temperature of 70deg F
B)The TempControl Company has a container that will reduce the temperature of a liquid from 200deg F to 110deg F in 60mins by maintaining a constant temperature of 60deg F.
C)the hot n cold Inc. has a container that will reduce the temperature of a liquid from 210deg F to 90deg F in 30mins by maintaining a constant temperature of 50deg F.
Your job is to make a recommendation as to which container to purchase . For this you will need Newton's Law of Cooling, whick follows:
u(t)=T+(u base 0 - T)e^kt k<0
In this formula,
T represents the temperature of the surrounding medium
u base 0 is the initial temperature of the heated object
t is the length of time in minutes
k is a negative constant
u represents the temperature at time t
1)Use Newtons's law of cooling to find the constant k of the formula for each container
2)Use a graphing utility to graph each relation.
3)How long does it take each container to lower the coffee temperature from 170deg F to 140deg F
4)How long will the coffee temperature remain between 120deg F and 140deg F
5)On the basis of this information, whick company should get the contract with McNewton's? What are your reasons?
6)Define "capital cost" and "operating cost". How might they affect your choice?