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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?

Guest 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

 

 

cool cool cool  

CPhill  Jan 16, 2018
edited by CPhill  Jan 17, 2018

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