The soft goods department of a large department store sells $175$ units per month of a certain large bath towel. The unit cost of a towel to the store is $$2\mathrm{.}50$ and the cost of placing an order has been estimated to be $$11\mathrm{.}75.$ The store uses an inventory carrying charge of $13\%$ of the unit cost. The store operates $280$ days per year.

Determine the following:

a$.$ What is the optimal order quantity?

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b$.$ What are the number of orders?

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c$.$ What is the cost of managing the inventory $($setup plus holding costs$)$

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d$.$ If the department store is open $280$ days per year, how many days are between orders?

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e$.$ If the lead time from the supplier takes $10$ days, what is the re$-$order point?

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f$.$ What is the total cost, including the cost of the inventory?

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