Question

fredv ber produces organic juice bottles. the revenue function ( r(p) ) and the expense function ( e(p) ) in terms of price ( p ) are given by:
( r(p)=200 p-4 p^{2} )
( e(p)=1,500-24 p )
what is the profit equation ( p(p) ) in terms of price ( p )?
( p(p)=4 p^{2}+224 p-1,500 )
( p(p)=-4 p^{2}+200 p )
( p(p)=-4 p^{2}+224 p-1,500 )
( p(p)=-4 p^{2}+176 p-1,500 )

Explanation:

Step1: Recall profit formula

Profit \(P(p)=R(p)-E(p)\)

Step2: Substitute \(R(p)\) and \(E(p)\)

\(P(p)=(200p - 4p^{2})-(1500 - 24p)\)

Step3: Remove parentheses

\(P(p)=200p - 4p^{2}-1500 + 24p\)

Step4: Combine like terms

\(P(p)=-4p^{2}+(200p + 24p)-1500=-4p^{2}+224p - 1500\)

Answer:

\(P(p)=-4p^{2}+224p - 1500\)