The cost of producing appliances is $C(x) = 300 + 2.2x^2$ where $x$ is the number produced per week.
If they are sold for $110 each, how many should be produced for maximum profit?
Profit = Revenue - Cost
$P(x) = R(x) - C(x)$
Let the cost of producing x number of units per week be $C(x) = 300 + 2.2x^2$ and the revenue $R(x) = 110x$ for selling x number of units.
Hence profit is $P(x) = 110x - 300 - 2.2x^2$.
To find the maximum profit, the derivative of $P(x) = 0$.
$P'(x) = 110 - 2.2x$
$110 - 2.2x = 0$
$x = 50$
The method above gives me x = 50 where the solution says 25. Is my understanding and approach correct?