Question

The profit P (in hundreds of dollars) that a company makes depends on the amount x (in hundreds of dollars) the company spends on advertising according to the model shown below. P = 260 + 70x – 0.5x^2. What expenditure for advertising will yield a maximum profit?

Answer 1

differentiate P with respect of x
\[\frac{{\rm d}P}{{\rm d}x} = 70 - x\]

set the derivative equal to zero

\[ 70 - x = 0 \]
\[x = 70 \]
that in hundreads of dollars, so result is $7000.