Chapter 16.1, Problem 45E

Cost

In a manufacturing process where $y=C(x)$ represents the cost of producing x units, the elasticity of cost is defined as $E(x)=\frac{\text{marginal}\text{cost}}{\text{average}\text{cost}}=\frac{C^{\prime }(x)}{C(x)/x}=\frac{x}{y}\frac{dy}{dx}$.

Find the cost function when the elasticity function is $E(x)=\frac{20x-y}{2y-10x}$ where $C(100)=500$ and $x\ge 100.$