Your monthly profit (in dollars) from selling magazines is given by $P ( x ) = 5 x + 2 \sqrt { x }$ where x is the number of magazines you sell in a month. If you are currently selling $x = 50$ magazines per month, find your profit and your marginal profit.
A) $P ( 50 ) = \$ 132.07 , P ^ { \prime } ( 50 ) = \$ 2.57$
B) $P ( 50 ) = \$ 260.00 , P ^ { \prime } ( 50 ) = \$ 0.49$
C) $P ( 50 ) = \$ 528.28 , P ^ { \prime } ( 50 ) = \$ 5.64$
D) $P ( 50 ) = \$ 260.00 , P ^ { \prime } ( 50 ) = \$ 5.14$
E) $P ( 50 ) = \$ 264.14 , P ^ { \prime } ( 50 ) = \$ 5.14$

Question

Your monthly profit (in dollars) from selling magazines is given by $P ( x ) = 5 x + 2 \sqrt { x }$ where x is the number of magazines you sell in a month. If you are currently selling $x = 50$ magazines per month, find your profit and your marginal profit.  
A) $P ( 50 ) = \$ 132.07 , P ^ { \prime } ( 50 ) = \$ 2.57$
B) $P ( 50 ) = \$ 260.00 , P ^ { \prime } ( 50 ) = \$ 0.49$
C) $P ( 50 ) = \$ 528.28 , P ^ { \prime } ( 50 ) = \$ 5.64$
D) $P ( 50 ) = \$ 260.00 , P ^ { \prime } ( 50 ) = \$ 5.14$
E) $P ( 50 ) = \$ 264.14 , P ^ { \prime } ( 50 ) = \$ 5.14$

Quizplus · Accepted Answer

To find the profit for selling 50 magazines, substitute $x = 50$ into the profit function: $P(50) = 5(50) + 2\sqrt{50} = 250 + 14.14 = 264.14$. For the marginal profit, differentiate $P(x)$ with respect to $x$ to get $P'(x) = 5 + \frac{1}{\sqrt{x}}$, then substitute $x = 50$: $P'(50) = 5 + \frac{1}{\sqrt{50}} = 5 + 0.14 = 5.14$.

Your Monthly Profit (In Dollars) from Selling Magazines Is Given P(x)=5x+2xP ( x ) = 5 x + 2 \sqrt { x }P(x)=5x+2x​

Your Monthly Profit (In Dollars) from Selling Magazines Is Given $P ( x ) = 5 x + 2 \sqrt { x }$