The director of the Blue Rose club must decide what to charge for a ticket to the club’s performance of The Music Man. If the price is set too low, the club will lose money, and if the price is too high, people won’t come. From past experience she estimates that the profit P from sales (in hundreds) can be approximated by `P(x)=-x^(2)+22x-40` where x is the cost of a ticket and `0le x le 25` thousand rupees.

What is the lowest cost of a ticket that would allow the club to break even.

Options

A. Rs 3 thousand
B. Rs 4 thousand
C. Rs 2 thousand
D. Rs 1 thousand

Answer

C

Explanation

At break even P(x) = 0, thus
`-x^(2)+22x-40=0`
`x^(2)-22x+40=0`
`(x-2)(x-20)=0`
`x=2,20`
Thus ( c ) is correct option.