Let x be the number of books that need to be sold, then for the cost of the production and the profit to be the same we can set the following equation:
[tex]30456+10x=21.75x\text{.}[/tex]Subtracting 10x from both sides of the equation we get:
[tex]30456=21.75x-10x,[/tex]adding like terms we get:
[tex]30456=11.75x\text{.}[/tex]Dividing by 11.75 we get:
[tex]x=2592.[/tex]Then the producer must sell 2592 books.
Answer: 2592.