$($Submit$,8$pts$)$ Suppose the annual demand $d=2000$ for a product is constant over

time. Further, suppose that there is no lead time and the fixed cost of placing an order

is $K=80.$ The interest rate at which money can be borrowed tends to rise with the capital

being borrowed, and the Finance Manager decides to define the stock$-$holding cost, $h,$ as an

increasing function of the average stock. Specifically they defines it as:

$h=a+b*($ average stock level$)$

where $a=10$ per unit per year and $b=0\mathrm{.}50$ per unit per year. Derive the optimality

condition for the order size $Q,$ and show that it reduces to solving a cubic equation. Note

that you do not need to solve this equation.