# Math Help - A word problem

1. ## A word problem

I've always had a problem with word problems...

1)A baseball team is trying to determine what price to charge for tickets. At a price of $10 per ticket, it averages 45,000 people per game. For every increase of$1, it loses 5,000 people. Everyone person at the game spends an average of $5 on concessions. What price per ticket should be charged in order to maximize revenue? 2) The volume of a rectangular box with a square base remains constant at 400 cm^3 as the area of the base increases as a rate of 15cm^3/sec. Find the rate at which the height of the box is decreasing when each side of the base is 19 cm long. (don't round answer) 2. Hello, dizizviet! Here's the first one . . . 1) A baseball team is trying to determine what price to charge for tickets. At a price of$10 per ticket, it averages 45,000 people per game.
For every increase of $1, it loses 5,000 people. Everyone person at the game spends an average of$5 on concessions.
What price per ticket should be charged in order to maximize revenue?

Let $x$ = number of $1 increases in the price of ticket. They will charge $(10 + x)$ dollars per ticket. For each $x$, there are $5000x$ fewer ticket sales. . . They will sell: . $(45000 - 5000x)$ tickets. So $(45000-5000x)$ tickets are sold at $(10+x)$ dollars each. The revenue from ticket sales is: . $R_1 \;=\;(10+x)(45000-5000x)$ dollars. The same $(45000-5000x)$ ticketholders will spend$5 each on concessions.

The revenue from concessions is: . $R_2 \;=\;5(45000-5000x)$ dollars.

Hence, the Total Revenue is: . $R \;=\;(10+x)(45000-5000x) + 5(45000-5000x)$ dollars.

. . and that is the function we must maximize.