SOLUTION: I have a big problem with a quadratic cost function for a firm. The cost function is 0.22222(q)^2 The price in the market is 8 (horizontal price line), and the point where th

Question 1010854: I have a big problem with a quadratic cost function for a firm.
The cost function is 0.22222(q)^2
The price in the market is 8 (horizontal price line), and the point where these two lines intersect is the profit maximum. It should be an output quantity of 6, this is what the graph shows.
But, when I use mathematics to solve it, I have to differentiate the profit function 8q - 0.22222(q)^2 (ends up as 8 - 0.44444q) and set it equal to zero....and I end up with a weird answer for q, namely 18.00018. Anyone with mathematic economic experience help me out? I know this goes a little beyond just quadratics.
Answer by rothauserc(4718) (Show Source): You can put this solution on YOUR website!
your profit function is a parabola that curves downward
**********************************************************************
1) taking the first derivative and setting it to 0, gives you the 'q' or x-coordinate which is a critical value(18.000180002) associated with the max profit
2) in this case, substitute the q value into your profit function -
the result is the max profit, 72.000720009

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