4. (15 pts) KAIST Press (KP) is considering publishing two different books. There are two types of costs for each book-i) the variable cost that occurs for every copy of the book published (cy for textbook 1 and cy for textbook 2), ii) the fixed cost that occurs only if at least one copy of the book is published (cf for textbook 1 and c for textbook 2), regardless of the amount of books published. For instance, if 10 copies of book 1 are published, the cost associated with textbook 1 is 10cy + cf. If no copies are produced, the cost is zero. The selling prices for copies of books 1 and 2 are p and p2, respectively. The produced amount of books will not exceed the forecasted demand for each book (d, and d for books 1 and 2., respectively). In addition, KP will publish book 2 only if it choose to publish book 1. Of course, the published amount of the books (x and x2 for books 1 and 2) should be integers. Formulate an integer programming problem to maximize the profit. You should maintain the linear structure. No point will be given without proper description of the objective function and constraints. You don't need to solve this problem.