Question

You own a hamburger franchise and are planning to shut down operations for the day, but you are left with 12 buns, 18

defrosted beef patties, and 16 opened cheese slices. Rather than throw them out, you decide to use them to make burgers
that you will sell at a discount. Plain burgers each require 1 beef patty and 1 bun, double cheeseburgers each require 2
beef patties, 1 bun, and 2 slices of cheese, while regular cheeseburgers each require 1 beef patty, 1 bun, and 1 slice of
cheese. How many of each should you make?
plain burgers
double cheeseburgers
regular cheeseburgers

Answer 1

Plain burgers: 12

Double cheeseburgers: 9

Regular cheeseburgers: 12

Explanation:

Let's use P, D, and R to represent the number of plain burgers, double cheeseburgers, and regular cheeseburgers, respectively.

Each plain burger requires 1 patty and 1 bun, so we can make a maximum of 12 plain burgers (since we have 12 buns).

Each double cheeseburger requires 2 patties, 1 bun, and 2 slices of cheese, so we can make a maximum of 9 double cheeseburgers with the available patties, buns, and cheese. (We have enough patties and buns for 18 burgers, but each double cheeseburger uses twice as many patties, so we divide the total number of patties by 2 to get the maximum number of double cheeseburgers we can make.)

Each regular cheeseburger requires 1 patty, 1 bun, and 1 slice of cheese, so we can make a maximum of 16 regular cheeseburgers with the available patties, buns, and cheese (since we have 16 slices of cheese).

To maximize our sales, we want to make as many of each type of burger as we can. Since we can only make 12 plain burgers, we should make all 12 of those. We can then make 9 double cheeseburgers (using 18 patties, 9 buns, and 18 slices of cheese), and 12 regular cheeseburgers (using 12 patties, 12 buns, and 12 slices of cheese).

So the final answer is:

Plain burgers: 12

Double cheeseburgers: 9

Regular cheeseburgers: 12