Inventory Problem Set. Please answer the following Assignment: You must show your work!

$1.$ In a single$-$period Newsvendor model, if the demand is normally distributed with a mean of $80$ and a standard deviation of $10,$ and the optimal service level is $\backslash (90\backslash \%\backslash ),$ what is the optimal order quantity?

$2.$ In a single$-$period Newsvendor model, if the demand is normally distributed with a mean of $80$ and a standard deviation of $20,$ and the optimal service level is $\backslash (90\backslash \%\backslash ),$ what is the optimal order quantity?

$3.$ Given the following inventory system: average weekly $(7$ days a week$)$ demand is $1000$ units with a standard deviation of $100$ units, review period is $28$ days $(4$ weeks$),$ lead time is $14$ days $(2$ weeks$)$ and the target service probability is $\backslash (90\backslash \%\backslash ).$ What is the appropriate level of safety stock?

$4.$ Given the following inventory system: average weekly $(7$ days a week$)$ demand is $1000$ units with a standard deviation of $100$ units, review period is $28$ days $(4$ weeks$),$ lead time is $14$ days $(2$ weeks$)$ and the target service probability is $\backslash (90\backslash \%\backslash ).$ Currently, inventory on hand is $50$ units. How many units should be ordered?

$5.$ Given the following inventory system: average weekly $(7$ days a week$)$ demand is $1000$ units with a standard deviation of $100$ units, review period is $28$ days $(4$ weeks$),$ lead time is $14$ days $(2$ weeks$)$ and the target service probability is $\backslash (90\backslash \%\backslash ).$ Currently, inventory on hand is $500$ units. How many units should be ordered?

$6.$ A product has an average daily demand of $400$ units with standard deviation of $100$ units. Lead$-$time is $1$ day. If management would like to satisfy all demand in $\backslash (80\backslash \%\backslash )$ of the cycles, what is the reorder point?

$7.$ A product has an average daily demand of $400$ units with standard deviation of $10\mathrm{.}0$ units. Lead$-$time is $1$ day. If management would like to satisfy all demand in $\backslash (80\backslash \%\backslash )$ of the cycles, what is the reorder point?

$8.$ A product sells for $\backslash (\backslash$$ $24\backslash )$ per unit and costs the retailer $\backslash (\backslash$$ $12\backslash )$ per unit, unsold units by the end of the season are salvaged for $\backslash$$$7\mathrm{.}0.$ Demand is normally distributed with a mean of $1000$ units and standard deviation of $100$ units. How many units should the retailer order?

$9.$ A product sells for $\backslash (\backslash$$ $24\backslash )$ per unit and costs the retailer $\backslash (\backslash$$ $12\backslash )$ per unit, unsold units by the end of the season are salvaged for $\backslash$$$9\mathrm{.}0.$ Demand is normally distributed with a mean of $1000$ units and standard deviation of $100$ units. How many units should the retailer order?