$2\mathrm{.}7.$ In Problem $2\mathrm{.}6,$ the Colonial House Furniture Company has investigated the manufacturing process to identify potential improvements that would improve quality. The company has identified four alternatives, each costing $$15,000,$ as follows:

Alternative

Improvement to Average Percentage Good Quality

$1$

Stage $1$: $93\%$

$2$

Stage $2$: $96\%.$ Stage $4$: $97\%$

$3$

Stage $5$: $97\%,$ Stage $6$: $98\%$

$4$

Stage $2$: $97\%$

Which alternative would result in the greatest increase in product yield?

Answer

Alternative $2,204$

Which alternative would be the most cost effective?

Answer

Alternative $2$

$2\mathrm{.}8.$ The Backwoods American company operates a telephone order system for a catalog of its outdoor clothing products. The catalog orders are processed in three stages. In the first stage, the telephone operator enters the order into the computer; in the second stage, the items are secured and batched in the warehouse; and in the final stage, the ordered products are packaged. Errors can be made in orders at any of these stages, and the average percentage of errors that occurs at each stage are as follows:

Stage

$\%$ Errors

$1$

$12\%$

$2$

$8\%$

$3$

$4\%$

If an average of $320$ telephone orders are processed each day, how many errorless orders will result?