(1) The HotBeverages Company has a cup that reduces thetemperature of a liquid from 200 F to 100 F in 30 minutes bymaintaining a constant temperature of 70 F.

(2) The BestSupplies Company has a cup that reduces thetemperature of a liquid from 200 F to 110 F in 25 minutes bymaintaining a constant temperature of 60 F.

(3) The MountainGrown Company has a cup that reduces thetemperature of a liquid from 200 F to 120 F in 20 minutes bymaintaining a constant temperature of 65 F.

You need to recommend which cup the restaurant shouldpurchase. Use the questions below to make a presentation of yourrecommendation with a documented explanation of the recommendationto the restaurant.

(a)Use Newton’s Law of Cooling to find a functionrelating to the temperature of the liquid over time for each cup.?(?) = ? ∙ ? ?? + ?? where ?(?) is the temperature of the objectafter a given time ? is a constant found from the initialtemperature of the object ? is a constant for the continuous rateof cooling of the object

(b)Graph the three functions on a single set of axisusing Excel.

(c)How long does it take each cup to lower the coffeetemperature from 200 F to 130 F?

(d)How long will the coffee temperature remain between110 F and 130 F for each cup?

(e)Eliminate one of the cups from your decision. Why didyou eliminate this cup?

(f) Complete the market analysis worksheet below for theremaining two cups. What is your final probability vector? How longwill it take to get to your final probability vector? What doesthis mean?

(g)Which company would you recommend to the restaurant?Explain your reasoning.

(h)How might the cost of the container affect yourdecision?