Problem $144706$:

Do not include anything other than numbers in your responses. For example, do not include comma or dollar sign in your numbers. As a rule of thumb, keep $2$ decimal places for larger numbers and $3$ decimal places for smaller numbers less than $1.$

The Colonial House Furniture Company manufactures four$-$drawer oak filing cabinets in six stages. In the first stage, the boards forming the walls of the cabinet are cut; in the second stage, the front drawer panels are woodworked; in the third stage, the boards are sanded and finished; in the fourth stage, the boards are cleaned, stained, and painted with a clear finish; in the fifth stage, the hardware for pulls, runners, and fittings is installed; and in the final stage, the cabinets are assembled. Inspection occurs at each stage of the process, and the average percent ages of good$-$quality units are as follows.

Stage Average percentage of good quality

$183$ percent

$288$ percent

$385$ percent

$490$ percent

$592$ percent

$687$ percent

The cabinets are produced in weekly production runs with a product input for $400$ units.

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 $1$: Only Stage $1$ quality improves to $87$ percent.

Alternative $2$: Stage $2$ quality improves to $92$ percent and Stage $4$ quality improves to $91$ percent. All the other quality percentages remain the same as the current situation.

Alternative $3$: Stage $5$ quality improves to $88$ percent and Stage $4$ quality improves to $94$ percent. All the other quality percentages remain the same as the current situation.

Alternative $4$: Only Stage $2$ quality improves to $96$ percent.

What is the yield if the company chooses to go with Alternative $1?$

What is the yield if the company chooses to go with Alternative $2?$

What is the yield if the company chooses to go with Alternative $3?$

What is the yield if the company chooses to go with Alternative $4?$

Which alternative would be the most cost effective?