Question

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? Do NOT enter the DOLLAR sign.

Answer 1

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 = (70,000 − 200P) × P = 70,000P − 200P2
• Costs = 700,000 + 110 x (70,000 − 200P) = 700,000 + 7,700,000 − 22,000P = 8,400,000 − 22,000P
• Profit = Sales-Costs = 70,000P − 200P2 − (8,400,000 − 22,000P) = −200P2 + 92,000P − 8,400,000

• Profit = −200P2 + 92,000P − 8,400,000

i.e. P2 – 460P = -42000

On solving the Quadratic, we get:

P – 230 = ±√10900 = ±104

P = 230 ± 104 = 126 or 334

It says that the profit is ZERO when the Price is $126 or $334

From the Above data, we can understand that the Profit goes up to a certain range and falls down again.

(For your visualization, I have attached the graph below)

So the best Price should be Midway between the Two Prices above. i.e.

Therefore the Best Price is : 126+104 = 230

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