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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

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




(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  

 Jan 16, 2018
edited by CPhill  Jan 17, 2018

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