The profit from making and selling x units of a product is given by P(x)= .05x^6+16x-600 dollars. How many units should be produced and sold in order to make a profit of $2200?
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.