Question

The revenue function​ R(x) and the cost function​ C(x) for a particular product are given. These functions are valid only for the specified range of values. Find the number of units that must be produced to break even. R(x)=200x- x2, C(x)=20x+6500, 0 less than or equals X less than or equals 100.The manufacturer must produce ---- units to break even.

Answer 1

The break even will; be only when R(X)= C(x)

hence

$200x-x^2=20x+6500$

Simplify;

$-x^2+180x-6500=0$

Solve for quadratic equation:-

$x=\frac{-180+\sqrt{180^2-4\left(-1\right)\left(-6500\right)}}{2\left(-1\right)}:\quad 50$

$x=\frac{-180-\sqrt{180^2-4\left(-1\right)\left(-6500\right)}}{2\left(-1\right)}:\quad 130$

As values for x should be >0 and <100, hence x= 50 is the value.