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A library lets a student borrow at most 4 books in all…

Try it on paper first. A hint, the key idea and the worked solution are here when you need them.

A library lets a student borrow at most $4$ books in all. A student chooses $x$ fiction books and $y$ non-fiction books, where $x$ and $y$ are whole numbers. Borrowing no book of a kind is allowed. The rule is $x + y \le 4$ with $x \ge 0$ and $y \ge 0$ . How many different choices $(x, y)$ are there, including borrowing nothing?

Need a reminder? The key ideaShow

The feasible region is the overlap of the regions of all the constraints, with $x \ge 0$ and $y \ge 0$ . It is bounded if a circle can enclose it, and unbounded if it runs on for ever. If the constraints contradict each other, the region is empty.

The worked solution

Have you tried it?

Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.

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