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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?

 Jun 16, 2018
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t = number of tickets

70 - (t-60) = price of tickets

 

t (70-(t-60)) >4200

t(-t +130) > 4200

-t^2 + 130t -4200 > 0

t^2-130t+4200< 0          Use Quadratic formula to find zeroes at t = 60    70

 

When t = 60       Sales 4200  

    When t = 70    sales = 4200      The question asks for the greatest number to be MORE than 4200       that would be when  t = 69   Sales= 4209

Here is a graph:

 Jun 17, 2018

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