A firm's revenue is $R(x) = 120x - x^{2}$ rupees and its cost is $C(x) = 40x + 600$ rupees for $x$ units. How many units give the greatest profit?

20 unitsCorrect answerYour answer40 unitsCorrect answerYour answer60 unitsCorrect answerYour answer80 unitsCorrect answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer B

Correct answer: B

Profit $P(x) = - x^{2} + 80 x - 600$ , and $P'(x) = 80 - 2 x = 0$ at $x = 40$ ; $P'' < 0$ , a maximum.
The best output is 40 units.

Worth noting

60 units maximises revenue alone; cost pulls the best output down.

Ten questions from Rate of Change, Marginal Cost & Revenue, at your own pace.

Ten questions from Rate of Change, Marginal Cost & Revenue, at your own pace.

A firm's revenue is R(x)=120x−x2R(x) = 120x - x^{2}R(x)=120x−x2 rupees and its cost is C(x)=40x+600C(x) = 40x + 600C(x)=40x+600 rupees for xxx units. How many units give the greatest profit?