Question

The cost function for a certain company is C = 40x + 800 and the revenue is given by R = 100x − 0.5x2. Recall that profit is revenue minus cost. Set up a quadratic equation and find two values of x (production level) that will create a profit of $800.

Answer 1

In order to do this, you have to find your profit equation and then set it equal to 800, which is the profit you're seeking.  when you subtract the cost from the revenue, the new equation (or the profit equation) is this:
 p(x)= -.5x^2 + 60x -800.  If you want your profit, p(x), to be $800, then you set your equation equal to 800 and solve it for x, the 2 values that will bring about that 800 profit. Those production levels, or values for x, are -22.5 and 142.5  Since you cannot have a negative production level, you need to produce 142.5 whatevers to make that profit.