Calculate break even point

kingjohann

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Dec 4, 2021
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Hello everyone,

I am a little overwhelmed by this problem, could anyone help me here?

You start a business that produces brick for the construction. You first investment is a machine that costs A€, with A=99,628. You also need to buy clay to produce your bricks: 1kg of clay per brick. The price of the clay decreases with the quantity you are buying. It starts at $20 per ton, and linearly decrease till $10 per ton if you buy more than 500 tons.

On average, the price for your bricks is B€ for 1000 bricks, with B=503. What is the break-even point (in the number of units sold)?

Hint 1: start by calculating the price of the clay according the quantity of clay you are buying, in tons. You can use t as the number of tons you are buying.

Hint 2: since each brick is made in pure clay and weighs 1kg, if you produce q bricks, you need q/1000 tons of clay: t=q/1000.
 
It starts at $20 per ton, and linearly decrease till $10 per ton if you buy more than 500 tons.
That does not sound 100% linear to me.
 
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