Question

The cost function for a certain company is C = 20x + 700 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 $700.

Answer 1

Answer:

The two values of production level are:

x = 20

or

x = 140

Step-by-step explanation:

Let's write the Profit equation by subtracting the cost function from the revenue one:

$Profit(x)=100\,x-0.5\,x^2-(20\,x+700)\\Profit(x)=-0.5\,x^2+80\,x-700$

Now, we set to find the production level "x" to give us a profit of $ 700:

$Profit(x)=-0.5\,x^2+80\,x-700\\700=-0.5\,x^2+80x-700\\0.5\,x^2-80\,x+1400=0$

So we solve this quadratic equation using the quadratic formula:

$x=\frac{80+/-\sqrt{80^2-4(0.5)(7700)}}{2\,*\,0.5} \\x=80+/-\sqrt{3600} \\x=80\,+/-\,60$

which gives two posible solutions: x = 20, or x = 140