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# Help needed on this question! Thank you!!!

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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?

Jan 16, 2018

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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

Jan 16, 2018
edited by CPhill  Jan 17, 2018