A charity organization had a fundraiser where each ticket was sold for a fixed price. They had to sell a few tickets just to cover necessary production costs of $1200\$1200 $1200 dollar sign, 1200 . After selling 200200 200 200 tickets, they had a net profit of $12,000\$12{,}000 $12,000 dollar sign, 12, comma, 000 . Let P(n)P(n) P(n) P, left parenthesis, n, right parenthesis denote the net profit from the fundraiser PP P P (measured in dollars) as a function of the number of tickets sold nn n n . Write the function's formula

We have been given that a charity organisation had to sell a few tickets just to cover necessary production costs of $1200. After selling 200 tickets, they had a net profit of $12,000.

Since we know that net profit is the difference between total revenue and total cost.

[tex]\text{Net profit}=\text{Total revenue- Cost}[/tex]

We can represent our given information in an equation to find the revenue collected from each ticket:

[tex]12000=200x-1200[/tex]

Let us solve for x by adding 1200 to both sides of equation.

[tex]12000+1200=200x[/tex]

[tex]13200=200x[/tex]

[tex]x=\frac{13200}{200}[/tex]

[tex]x=66[/tex]

Therefore, the revenue collected from selling each ticket is $66.

Now let us write the net profit, P(n), from fundraiser as the function of number of tickets sold,n.

The revenue from selling n tickets will be 66n.

Production costs = 1200

[tex]P(n)=66n-1200[/tex]

Therefore, our desired function will be: [tex]P(n)=66n-1200[/tex].