Capacity Planning: Expansion

$>D=5000$

$>r=16\%$

$>f(y)=0\mathrm{.}0107y^{0\mathrm{.}62}$

$\frac{r{x}^{**}}{e^{r{x}^{**}}-1}=a$

$\frac{0\mathrm{.}16x^{**}}{e^{0\mathrm{.}16x^{**}}-1}=0\mathrm{.}62$

$x^{**}=5\mathrm{.}625$ years

Capacity expansion: $x^{**}D=28125$ units

A company estimates that the cost of new capacity additions follows the function $f(y)=$

$0\mathrm{.}0358y^{0\mathrm{.}66},$ where $y$ is the number of units and $f(y)$ in millions of dollars. Demand is

increasing at a rate of $3,500$ units per year. The company uses a $10\%$ per year interest rate. What

is the present value of the cost of the next nine capacity additions?