Question

The profit function for a new product is given by p(x) = -4x^2+28x-40, where x is the number sold in thousands. How many items must be sold for the company to break even?

Answer 1

The break even point is when profit is equal to zero, or in this case when p(x)=0

4x^2-28x+40=0

4(x^2-7x+10)=0

4(x^2-2x-5x+10)=0

4(x(x-2)-5(x-2))=0

4(x-5)(x-2)=0

So the break even points are when x=2 and 5, which is when 2000 and 5000 units are sold.