Let us consider that the enjoyment of eating a Cadbury egg is 25 units of happiness, and the enjoyment of having a Cadbury egg to eat later is given by the function 20-3t units of happiness per day where t is the number of days since you acquired the Cadbury egg. This function decreases as t increases because of the increased risk that the Cadbury egg will melt.

a) Find the equation in terms of t that gives the total happiness coming from the ownership and consumption of a Cadbury egg.

Answer: 25 plus the integral of (20-3t dt)

b) If one eats the Cadbury egg at t=7, how much happiness has one gotten from the Cadbury egg over the week?

Answer: 25 + the integral of (20-3t dt) from 0 to 7=25+(20t-(3t^2)/2) evaluated at 7 and 0=25+(140-73.5)-(0)=91

c)If one eats the Cadbury egg at t=5, how much happiness has one gotten from the Cadbury egg over the five days?

Answer: 25+ the integral of (20-3t dt) from 0 to 5=25+(20t-(3t^2)/2) evaluated at 5 and 0=25+(100-37.5)-(0)= 87.5

d) When should you eat your Cadbury egg in order to maximize Cadbury egg enjoyment?

Answer: t=6 2/3, because that is the highest value of t for which (20-3t) is positive, and the integral of (20-3t dt) is therefore increasing.

e) When are you going to eat that Cadbury egg?

Answer: t=0.

Note to self: You’re really supposed to save Easter candy until Easter, you know.

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