The cost function for a certain company is c = 50x + 600 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 $600.

The quadratic equation is:   and the two values of will be 40 and 60 that will create a profit of $600.

Explanation

The cost function is:   and

The revenue function is:  

As the profit means , so the Profit function will be....

So, the quadratic equation is:  

Now for creating a profit of $600 means, we will plug into the above equation. So.....

Now applying zero-product property.....

So, the two values of will be 40 and 60 that will create a profit of $600.

x/3-10=8

x/3=18

x=48