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James owns a cafe. A mathematical model connecting profit from selling coffee (in dollars) and x, the price per cup of coffee (in dimes) is #p(x)= -x^2+ 35x+ 34#, how do you find the profit per day if the price per cup of coffee is $1.80?

Answer 1

#$340#

If a cup of coffee costs #$1.80# then it costs #18# dimes.

The profit function #p(x)=-x^2+35x+34# gives the the profit #p# in dollars given a price per cup #x# in dimes.

Substituting #18# (dimes) for #x# gives #color(white)("XXX")p(18)=-(18^2)+(35xx18)+34# #color(white)("XXXXXX")=-324+360+34# #color(white)("XXXXXX")=340# (dollars)

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Answer 2

Jace Anderson

To find the profit per day when the price per cup of coffee is $1.80, substitute$ 1.80 for x in the profit function p(x). So, p(18) = -18^2 + 35(18) + 34. Calculate the value of p(18) to find the profit per day.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.