I added all of them and got the total joint production costs as $26,000 however it is wrong and I dont understand why the book says $23,000 as we are incurring all these costs in the production process
If you are copying everything correctly, then neither you nor your book are correct!
If you start with inventory of 1,000 and then spend another 10,000 and another 12,000, then the total cost is $23,000. If some of the material is left in closing inventory, then only 20,000 (23,000 – 3,000) was spent on what was actually produced.