Determining quadratic function of this word problem. A tour company offers back country hiking excursions at $160 per person for groups up to 50. For groups larger than 50, the company will reduce the cost of every ticket by $2 for each person in excess of 50. What size of group would produce the greatest revenue?

gfresh86iop

gfresh86iop

Answered question

2022-11-19

Determining quadratic function of this word problem
A tour company offers back country hiking excursions at $160 per person forgroups up to 50. For groups larger than 50, the company will reduce the cost of every ticket by $2 for each person in excess of 50. What size of group would produce the greatest revenue?
I'm not worried about finding out what the size of the group is that produces the greatest revenue. What I want to know is what the equation for this is. I was able to figure out this equation:
f ( x )   =   160 x 2 ( x 50 )   ,
where x is the number of people and f(x) is the revenue. But that's a linear function and we're doing quadratic functions. So, There should be an exponent and I'm thinking there's more to this question than I see? Or is it a linear function?

Answer & Explanation

Hailee West

Hailee West

Beginner2022-11-20Added 15 answers

Explanation:
Note that if you have n > 50 people, your revenue will be ticket price for each person (which is 160 2 ( n 50 )) times the number of people n, i.e. ( 160 2 ( n 50 ) ) n.

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