Thread: Multiple choice price and quantity

1. Multiple choice price and quantity

Maths multiple choice question?

Each week, a company can sell x units of its product at a price of p dollars each,
where p = 250 - 4x. The total cost of producing x units is 4800 - 70x. Note that
revenue is equal to price times quantity. What quantity or quantities should the
company produce if it aims to break even?
(a) 20 units;
(b) 60 units;
(c) 20 or 60 units;
(d) 40 units.

2. Hello marie7
Originally Posted by marie7
Maths multiple choice question?

Each week, a company can sell x units of its product at a price of p dollars each,
where p = 250 - 4x. The total cost of producing x units is 4800 - 70x. Note that
revenue is equal to price times quantity. What quantity or quantities should the
company produce if it aims to break even?
(a) 20 units;
(b) 60 units;
(c) 20 or 60 units;
(d) 40 units.
The company sells $\displaystyle x$ units at $\displaystyle (250-4x)$ dollars each. The revenue from this is $\displaystyle x \times (250-4x)$. If they break even, then this revenue is equal to the total production cost, which is $\displaystyle (4800-70x)$ dollars. So:

$\displaystyle x(250-4x)=4800-70x$

$\displaystyle \Rightarrow 250x-4x^2 = 4800-70x$

$\displaystyle \Rightarrow 4x^2 -320x+4800=0$

$\displaystyle \Rightarrow x^2-80x+1200=0$

$\displaystyle \Rightarrow(x-20)(x-60)=0$

$\displaystyle \Rightarrow x = 20$ or $\displaystyle x=60$