Question

The total cost of production of $n$ items is given by $C=7n+350$. The selling price of an item is 12$.Whichofthefollowinginequalitiesgivesallpossiblevaluesof$n$ company will make a profit?

• A. $n<70$
• B. $n<84$
• C. $n>70$
• D. $n>84$

Answer 1

Answer: (C)

$n>70$

Given, cost of production of n items is $=$ $C=7n+350$
Selling price of an item is $\$12$
Cost of production of one item will be $=$ $\frac{7n+350}{n}$
Profit company will make by selling an item is,
$12-\frac{7n+350}{n}$
$\Rightarrow \frac{12n-(7n+350)}{n}=0$
$\Rightarrow 12n-7n-350=0$
$\Rightarrow 5n=350$
$\Rightarrow n=70$
So, in the given inequalities $n>70$ suits, the possible value of $n$ company will make a profit.