n the coffee house will not make a profit. Determine what the coffee house needs to charge in order to break even (make a profit of $0.00 ). c) If the cost of a cup of coffee is too high then not enough people will want to buy coffee. As a result, the weekly profit will be $0.00 . Determine what the coffee house would have to charge for this to happen (the profit to be $0.00 ).
A coffee house finds that its weekly profit ? (measured in dollars) as a function of the price ? (measured in
dollars) it charges per cup of coffee is given by the function ?, defined by ?(?) = ―1000?2 +4680?―4130
where ?= ?(?) .
a) Determine the maximum weekly profit and the price of a cup of coffee that produces that maximum
profit.
b) If the cost of a cup of coffee is too low then the coffee house will not make a profit. Determine what
the coffee house needs to charge in order to break even (make a profit of $0.00 ).
c) If the cost of a cup of coffee is too high then not enough people will want to buy coffee. As a result, the
weekly profit will be $0.00 . Determine what the coffee house would have to charge for this to happen
(the profit to be $0.00 ).
d) The profit function for Delish Coffee (another coffee house) is defined by the function ? where ?(?)
= ?(?―2.5) . Does the function ? have at the same maximum value as ? ?
e) What is the price per cup of coffee that Delish Coffee must charge to produce a maximum profit?
Explain.
f) Describe the meaning of ?(?) = ?(?) ―115 and then compare/contrast the maximum value for each
function.
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