Answer:
63 units
Step-by-step explanation:
The profit function P(x) is given by the revenue function minus the cost function:
[tex]P(x) = R(x) - C(x)\\P(x) = 34ln(x+5)-\frac{x}{2}[/tex]
The number of units sold 'x' for which the derivate of the profit function is zero, is the number of units that maximizes profit:
[tex]P(x) = 34ln(x+5)-\frac{x}{2}\\P'(x) =0= \frac{34}{x+5}-\frac{1}{2}\\x+5=68\\x=63\ units[/tex]
The number of units that should be manufactured so that profit is maximum is 63 units.
