The cost function for a certain company is C=70x+200 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 $200.

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The cost function for a certain company is  C=70x+200  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 $200.

Jennifer Hill · Accepted Answer

Step 1  The cost function for a eartain company is  C=70x+200  and the revenue is given by  R=100x−0.5x2  Step 2  Given that  C=79x+200 and R=100x−0.5x2  profit=revenue−cost  =100x−0.5x2−70x−200  =−0.5x2+30x−200  If profit =$200  ∴−0.5x2+30x−200=200  ⇒−0.5x2+30x−200−200=0  ⇒−0.5x2+30x−400=0  ⇒0.5x2−30x+400=0  ⇒x=30±(30)2−4×(0.5)×(400)2−(0.5)  ⇒x=30±900−800{1}  ⇒x=30±100  ⇒x=30±10  Step 2  ⇒x=30+10, 30−10  ⇒x=40, 20  Hence, two values of x are 20 and 40

The cost function for a certain company is C=70x+200 and the revenue

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