Question

Let total revenue received from the sale of $x$ units of a product is given by $R\left(x\right)=12x+2x^2+6.$
Then the actual revenue from selling the ${51}^{\text{st}}$ item is

[2 marks]

• A. $214$
• B. $202$
• C. $212$
• D. $200$

Answer 1

The correct option is A $214$

Given : $R\left(x\right)=12x+2x^2+6$
Actual revenue from selling the ${51}^{\text{st}}$ item
$=R\left(51\right)-R\left(50\right)$
$=\left\{12\right(51)+2(51{)}^2+6\}-\left\{12\right(50)+2(50{)}^2+6\}$
$=12(51-50)+2({51}^2-{50}^2)+(6-6)$
$=12+2(51-50)(51+50)$
$=12+202$
$=214$