The price of an airline ticket to Zua Zua island on a chartered flight with \(200\) seats is set at \(\$500\) for the

[BTGmoderatorLU]

The price of an airline ticket to Zua Zua island on a chartered flight with \(200\) seats is set at \(\$500\) for the first \(50\) tickets sold. Once \(50\) tickets are sold, the price of each ticket is set at \(\$600.\) What is the least number of tickets that must be sold to realize revenue of at least \(\$30,000?\)

A. \(50\)
B. \(57\)
C. \(58\)
D. \(59\)
E. \(60\)

The OA is D

[SanjuSimpleson]

Let x be the least number of tickets sold to realize the needful, then $$50\times500\ +\ 600\ \left(x\ -\ 50\right)\ge30,000$$, solving gives $$x\ \ge\frac{350}{6}$$, so a minimum of 59 tickets must be sold.