At a certain amusement park, there is a bulk discount for tickets. If you buy up to 60 tickets in one order, the price for each ticket is $70.However if you buy more than 60 tickets in a single order, the price of every ticket is reduced by $1 for each additional ticket bought. If *t* is the number of tickets bought in bulk at one time, what is the largest *t* which will bring the amusement park a profit greater than $4200?

Guest Jan 16, 2018

#1**+1 **

These are always a little difficult

Here's the way I might approach it....

Let x be the number off additional tickets that will sell for every price decrease of $1

No. of tickets * Price per ticket = Revenue

So.....

(60 + x) (70 - 1x) > 4200

Look at the graph here : https://www.desmos.com/calculator/bzxbplskdb

It shows that when x = 5, the max profit is $4225

So.....the park maximizes the profit when it sets its price at (70 - 5) = $65 for a bulk purchase of t tickets (60 + 5) = 65 tickets .....so t = 65

CPhill
Jan 16, 2018