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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

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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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