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.

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mberisso mberisso · Answer 1 · 2020-06-21T04:15:10+02:00

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:

[tex]Profit(x)=100\,x-0.5\,x^2-(20\,x+700)\\Profit(x)=-0.5\,x^2+80\,x-700[/tex]

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

[tex]Profit(x)=-0.5\,x^2+80\,x-700\\700=-0.5\,x^2+80x-700\\0.5\,x^2-80\,x+1400=0[/tex]

So we solve this quadratic equation using the quadratic formula:

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

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