EMILE : Enseignement d'une Matière Intégrée à une Langue Étrangère

You have designed a new style of sports bicycle! Now you want to make lots of them and sell them for profit.

Your costs are going to be:

• \$700.000 for manufacturing set-up costs, advertising, etc

• \$110 to make each bike

Based on similar bikes, you can expect sales to follow this "Demand Curve":

• Unit Sales = 70.000 − 200P

Where "P" is the price.

For example, if you set the price:

• at \$0, you just give away 70.000 bikes

• at \$350, you won't sell any bikes at all

• at \$300 you might sell 70.000 − 200×300 = 10.000 bikes

So ... what is the best price? And how many should you make?

Let us make some equations!

How many you sell depends on price, so use "P" for Price as the variable.

• Unit Sales = 70.000 − 200P.

• Sales in Dollars = Units × Price =_________________

• Costs = _______________________

• Profit = Sales-Costs =_______________________

• Profit = −200P2 + 92.000P − 8.400.000

Yes, a Quadratic Equation. Solve this one and comment.

### More problems:

1. Find m in order to get 1 as solution to mx² - 2(m-1)x + 3m + 2 = 0 . Calculate the 2nd solution.

2. A farmer wants to make a rectangular pen for his sheep. He has 60m fencing material to cover three sides with the other side being a brick wall. How should he use the fencing material to maximize the space for his sheep? How should he choose length and width of the pen to achieve his objective?

3. The shortest side of a right-angled triangle is 6cm shorter than its hypotenuse. The difference in length of other two sides is 3cm. If the shortest side is n-3, show that n2 = 12n. Hence, find n.

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