Now that Christmas is over, we can sit back and relax a little. We can play with new toys, or just sit back and relax. Can you determine the best way to spend your day? Based on the scenarios below, how would you choose to manage your time?

Throughout the quiz, we'll assume that you have 16 hours in the day to use for things other than sleeping.

## #1.

- Suppose that all you want to do today is either sit and talk with your family or look online for exciting posts like this one. The amount of enjoyment you get out of each can be modeled by \(E(f)=2f-.05f^{2}\), where \(f\) is the amount of time spent with family. The enjoyment you get out of browsing the internet can be modeled by \(E(w)=w-.05w^{2}\), where \(w\) is the amount of time spent on the internet. How much time should you spend doing each in order to maximize your enjoyment for they day?

## #2.

- Suppose that all you want to do today is either sit and talk with your family, look online for exciting posts like this one, or watch Doctor Who. The amount of enjoyment you get out of each can be modeled by \(E(f)=f-.2f^{2}+.5w-.1w^{2}+d+.1wd-.1d^{2}\), where \(f\) is the amount of time spent with family, \(w\) is the amount of time spent on the internet, and \(d\) is the amount of time watching Doctor Who. How much time should you spend doing each in order to maximize your enjoyment for they day?

You should spend

hours playing with your family.

hours playing with your family.

You should spend

hours online.

hours online.

You should spend

hours watching Doctor Who.

hours watching Doctor Who.

## #3.

- Suppose that you received a drone, and The Reckoner Series books. For every hour flying your drone, you have to stop to charge it for 36 minutes. You have been instructed that you will only be able to play with the drone if you read. In particular, if you read for a certain amount of time, you can play with the drone three times as long as you read. Letting \(d\) be the time spent flying the drone and \(r\) be the time spent reading, your enjoyment level can be modelled by \(E(d,r)=2d+r\). How much time should you spend playing with each object in order to maximize your enjoyment for the day?

## #4.

- Suppose that, as in the last problem, you received a drone, and The Reckoner Series books. However, you also received Super Smash Brothers. You will still need to charge your drone as before, but the reading restriction applies to total time spent playing the game or flying the drone. Letting \(s\) be the time spent playing Smash Brother and \(d\) and \(r\) as before, your enjoyment level can be modelled by \(E(d,s,r)=2d+3s+r\). How much time should you spend playing with each object in order to maximize your enjoyment for the day?

You should spend

hours playing with the drone.

hours playing with the drone.

You should spend

hours reading.

hours reading.

You should spend

hours playing Smash Brothers.

hours playing Smash Brothers.

## #5.

- Instead of being able to relax today, you have a lot you need to get done. You have the following list of chores to run
- Exchange the clothes you received that didn't fit.
- Drop off you garbage because it won't wait until garbage day.
- Get more groceries because, surprisingly, there were no left overs.

Home | Cl. 1 | Cl. 2 | Garb. | Groc. | |
---|---|---|---|---|---|

Home | 0 | 7 | 12 | 10 | 8 |

Cl. 1 | 7 | 0 | 7 | 8 | 11 |

Cl. 2 | 12 | 7 | 0 | 5 | 9 |

Garb. | 10 | 8 | 5 | 0 | 6 |

Groc. | 8 | 11 | 9 | 6 | 0 |

When filling in the answers below, submit **1** for Clothing 1, **2** for Clothing 2, **3** for Garbage and **4** for Grocery.

Beginning at home, our next stop will be
.

After that, our second stop will be
.

Our third stop will then be
.

Then our fourth stop will be
.

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