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Coastal Soda Sales has been granted exclusive market rights to the upcoming Beaufort Seafood Festival. This...

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Basic Math

Coastal Soda Sales has been granted exclusive market rights tothe upcoming Beaufort Seafood Festival. This means that during thefestival Coastal will have a monopoly, and it is anxious to takeadvantage of this position in its pricing strategy. The dailydemand function is

p = 2 − 0.0004x

and the daily total cost function is

C(x) = 800 + 0.2x + 0.0001x2

where x is the number of units.

(a) Determine Coastal's total revenue and profit functions.

R(x)=
P(x)=



(b) What profit-maximizing price per soda should Coastalcharge?
$  per soda

How many sodas per day would it expect to sell at this price?
sodas per day

What would be the daily profits?
$  per day

(c) If the festival organizers wanted to set an economicallyefficient price of $1.25 per soda, how would this change theresults from part (b)? (Round your answer for daily profits to thenearest cent.)

sodas per day it would expect tosell    sodas per day
daily profits    $per day

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