Question

A cottage industry produces a certain number of toys in a day. The cost of production of each toy (in rupees) was found to be 55 minus the number of toys produced in a day. On a particular day, the total cost of production was Rs.750. If x denotes the maximum number of toys produced that day, find x.

Answer 1

Let the number of toys produced on that day $=x$

Cost of production of each toy that day $=55-x$

On a particular day, total cost of production was $750$

$x(55-x)=750$

$⟹x^2-55x+750=0$

$⟹x^2-30x-25x+750=0$

$⟹x(x-30)-25(x-30)=0$

$⟹x=25,30$

$\therefore$ Maximum number of toys produced that day $=30$