Question $2($Capacity planning$)$ Given the following possible demand and probability of demand, calculate the optimal production volume? Assume that the Inventory holding cost $=10\%,$ Margin $=$ $$100,$ Cost of Production $=$ $$100.$

$$

Demand

Probability

$200$

$0\mathrm{.}09$

$220$

$0\mathrm{.}09$

$240$

$0\mathrm{.}19$

$260$

$0\mathrm{.}15$

$280$

$0\mathrm{.}3$

$300$

$0\mathrm{.}15$

$320$

$0\mathrm{.}01$

$340$

$0\mathrm{.}01$

$360$

$0\mathrm{.}01$