Quadratic Word Problems

Question

The organizers of a spring fair have developed a profit relation (P) that depends on the ticket price (t) charged per person. The profit is modeled using the relation P=-37t^2+1258t-7700. 

 

A) create a table of value from 8 to 26 in 2 ticket increments. 

b) what is the ticket price that gives the max profit ? what is the max profit ? 

c) what ticket price will have a profit of zero ? 

Answer 1

A) Create a table with T on the left and P on the right. T increases by increments of 2 all the way to 26. The value for P can be found by substituting the value for t  into the relation given for profit.

 

B)

 

We need to differentiate the above relation and set it equal to zero in order to find the ticket price that  gives the max profit

 

dP / dT = 74t + 1258

 

 

74t + 1258 = 0

 

t = 1258 / 74

 

= 17

 

In order to find the max profit we need to plug in the value for t into the relation

 

P =- 37 (17)^2 + 1258(17) - 7700

 

= $2993

 

The max profit we can obtain from the sale of tickets is $2993

 

C)

 

Set P = 0 in the above relation and then use the quadratic equation to find the roots . Keep in mind that the answer would be a positive real value since the cost of a ticket cannot be negative.