The cost function for a certain company is C=60x+300 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 $300.

Question

The cost function for a certain company is  C=60x+300  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 $300.

Vaing1990 · Accepted Answer

Step 1  P(x)=R(x)−C(x)  Where P = Profit Function, C = cost function, R = revenue function  Step 2  R(x)−C(x)=300  ⇒100x−0.5x2−60x−300=300  ⇒40x−0.5x2−600=0  ⇒40x−510x2−600=0  ⇒400x−5x2−6000=0  ⇒5x2−400x+6000=0  ⇒x2−80x+1200=0  ⇒x2−60x−20x+1200=0  ⇒x(x−60)−20(x−60)=0  ⇒(x−60)(x−20)=0  Rither, x−60=0  ⇒x=60  or, x−20=0  x=20  ∴ The two values of x with be 60, 20 that with create a profit of Rs 300

The cost function for a certain company is C=60x+300 and the revenue

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