Mini-scenarios – Multiple Chapters

Morden Shapiro

Scenario 1

You have $9.65 of change in your pocket. You are in the airport about to board your flight home, where you will not be able to purchase items in $ currency. You want to buy as many “pieces of something” as you can afford with that change. You’re at the candy bar. They have a bin full of pieces of candy wrapped individually. There are three sizes: small, medium and large. They cost: Small $0.05 cents per piece; Medium $0.10 per piece; Large $0.15 per piece.

In mathematical terms determine how many pieces of each size should you purchase in order to achieve your goal and be happy on your flight?

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Scenario 2

Your supplier has just sent you an invoice for your most recent purchase of raw materials. The total invoice amount is $462.30. The invoice offers you the following payment terms:

  • The total invoice amount is due and payable within 30 days;
  • If you pay the total invoice amount within 10 days then you can deduct an amount of 15% of the total invoice amount;
  • If you pay after the 30 days then you will begin to pay simple interest at the annual rate of 20% per annum (computed on a daily basis) on the total invoice amount beginning on the 31st

In mathematical terms describe each of those conditions.

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Scenario 3

You are at an industry trade show. One of the suppliers has a booth at which they are demonstrating a new office device which you would very much want to have for your office. The show special allows you to purchase the device for the total cost of $1,900.00 (taxes included). In order to hold the show price, you need to leave a credit card deposit in the amount of $500.00

You have a card which is currently at its credit limit. You have no cash on hand. You call the credit card company and are told “We can authorize the transaction BUT because you are at the limit and tomorrow is the due date (you have every intention of paying the total balance tomorrow) we will deal with this as a cash advance and not a credit charge. Cash advances cost 18% per annum compounded daily.

In mathematical terms determine how much of a saving the show price must represent from the “normal” non-show price in order to make this a worthwhile transaction for you.

 

Attribution: Case study by Morden Shapiro (Ontario Tech University), published under Creative Commons Attribution-NonCommercial-ShareAlike licence (CC-BY-NC-SA)

Any modifications to this case study may affect its solvability and caution is advised.

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