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(Solved): The demand for an insulated stainless steel bottle is modeled by the function f(p)=\sqrt(523-0.4p^(2 ...
The demand for an insulated stainless steel bottle is modeled by the function
f(p)=\sqrt(523-0.4p^(2)),0<=p<=30
where f(p) is the quantity in thousands of bottles produced weekly and p is the price,
in dollars, of each bottle.
(a) Write out f^(')(p) by doing the following:
Rewrite f(p) in power form.
Then demonstrate the general power rule to find the derivative. Do not
simplify your answer.
(b) Write out the function E(p).
(c) Find E(25). Is the price of $25 inelastic, elastic, or does it have unit elasticity?
(d) If the company is charging $25 for a stainless steel bottle, should they raise the
price or lower the price in order to increase their revenue? Give a reason for your
choice.