On the average, a company has a work$-$in$-$process lead time of $10$ weeks and annual cost

of goods sold of $$10$ million. Assuming that the company works $50$ weeks a year:

$($a$)$ What is the dollar value of the work$-$in$-$process?

$($b$)$ If the work$-$in$-$process could be reduced to $5$ weeks and the annual cost of carrying

inventory was $20\%$ of the WIP inventory value, what would be the annual savings?

$2.$ AF sales are $$10$ million. The company spends $$3\mathrm{.}5$ million for purchase of direct

materials and $$2\mathrm{.}5$ million for direct labor; overhead is $$3\mathrm{.}5$ million and profit is

$$500,000.$ Direct labor and direct material vary directly with sales, but overhead does not.

The company wants to double its profit.

a$.$ By how much should the firm increase annual sales?

b$.$ By how much should the firm decrease material costs?

c$.$ By how much should the firm decrease labor cost?