Assume that it takes four hours of labor time to paint a room and three hours to sand a floor. If all 24 hours were spent painting, how many rooms could be painted by one person? If a decision were made to sand two floors, how many painted rooms would have to be given up? Illustrate with a production possibilities curve

Well, let me put on my painting pants and clown shoes to answer your question!

If it takes four hours to paint one room, and a person has 24 hours available, we can divide the total time by the time it takes to paint one room: 24 hours / 4 hours per room = 6 rooms.

So, one person could paint 6 rooms in 24 hours. That's a lot of paint!

Now, let's say they decide to sand two floors instead. Since it takes three hours to sand one floor, sanding two floors would require 3 hours per floor x 2 floors = 6 hours.

If they spend 6 hours sanding, that leaves them with 24 hours - 6 hours = 18 hours for painting.

Since it takes 4 hours to paint one room, we can divide the remaining time by the time it takes to paint one room: 18 hours / 4 hours per room = 4.5 rooms.

But wait, you can't paint half a room! So, they would have to give up painting 4 rooms in order to sand two floors.

To illustrate this situation on a production possibilities curve, we would have two axes: one for the number of rooms painted and one for the number of floors sanded. We would draw a curve that shows the trade-off between painting rooms and sanding floors. As you move along the curve from one point to another, you're sacrificing some rooms to gain more floors or vice versa.

I hope that puts a smile on your face!

To answer the first question, we need to determine how many rooms can be painted in 24 hours. Given that it takes four hours to paint one room, we divide the total available time (24 hours) by the time needed to paint a room.

24 hours / 4 hours per room = 6 rooms

Therefore, one person can paint a total of 6 rooms in 24 hours.

Now, let's move on to the second question. We need to find out how many painted rooms would have to be given up if two floors were sanded. Since it takes three hours to sand a floor, we would need to subtract the time spent sanding floors from the total 24-hour time frame.

24 hours - (2 floors * 3 hours per floor) = 24 hours - 6 hours = 18 hours

Now, we can calculate the number of rooms that can be painted in the remaining 18 hours. Using the same formula as before:

18 hours / 4 hours per room = 4.5 rooms

Since we cannot have half a room, we need to round down to the nearest whole number. Therefore, if two floors were sanded, one person would have to give up painting 4 rooms in exchange.

To illustrate this scenario on a production possibilities curve (PPC), we can plot the number of painted rooms on the y-axis and the number of sanded floors on the x-axis. We would start with a point at 6 rooms and 0 floors (representing the initial scenario), and then move to a point at 2 floors and 4 rooms (representing the scenario after sanding two floors). By connecting these two points, we can trace a downward slope representing the trade-off between painting rooms and sanding floors.