Suppose a vendor sells seat tickets and floor tickets to a concert. She would like to determine the price she should charge for each ticket type to meet her needs. She can admit 500 people on the floor and 250 people for seats. She needs a concert revenue of $25,750 in order to cover her costs and to take home a little bit of profit. Additionally, the average of the two ticket prices should be $20, so that the average price that shows up on her website sounds appealing to concert-goers. Assume she will fill up the venue.

In regards to mathematical solutions that can be implemented in the real world, x = the price of seat tickets ($) and y = the price of floor tickets ($), we found that an appropriate model for the constraints given consisted of the following two mathematical equations:

500x + 250y = 25,750

(x + y)/2 = 20

This resulted in the solution set (x,y) = (63,-23), which does not make practical sense since we cannot charge -$23 for a ticket.

The problem has to be rectified by "tweaking" the constraints to produce a viable solution to the problem at-hand.

I need to address within my response that:

**If we only change the: a.) number of floor tickets b.) number of seat tickets c.) revenue d.) average price of a ticket

what is the reasonable possibility for the price and what is the resulting solution for each of the listed above in a-d?

Each part is in need of a clear explanation with detail and must be graphed even though the outcomes won't make sense in real-life terms I am trying to figure how this gets pieced together.