Let total amount earned per day be T, and x be price increase.
T
= (8 + x)(360 - 20x)
= 2880 + 360x - 160x - 20x^2
= -20x^2 + 200x + 2880
T' = -40x + 200
Setting T' to zero, we have:
-40x + 200 = 0
40x = 200
x = 200 / 40
x = 5
T'' = -40 < 0, so we have a local max at x = 5.
Since T is a quadratic equation, this means that this local max is also an absolute max.
8 + x = 8 + 5 = 15
Hence, optimal proce is $13