P(x)= .05x^6+16x-600 -----??

0.05x^6?

I assume that should be

P(x) = 0.05x^2 +16x -600

So if profit = $2200,

2200 = 0.05x^2 +16x -600

0.05x^2 +16x -600 -2200

0.05x^2 +16x -2800 = 0

Divide both sides by 0.05,

x^2 +320x -56,000 = 0

Using the Quadratic Formula,

x = {-320 +,-sqrt[(320)^2 -4(1)(-56,000)]} / 2(1)

x = {-320 +,-571.3} /2

x = 125.7 or -445.7 units

Reject the x = -445.7 because negative number of units cannot be produced.

Therefore, produce and sell 126 units to get about $2200 profit.