Antaplu is committed to its quality program: it works with all areas of the company establish sound quality programs within reasonable budget guidelines. For $2013,$ it has budgeted $$1\mathrm{.}000,000$ for prevention costs and $$900\mathrm{.}000$ for appraisal costs. internal failure has a budget of $$100$ per failed item, while external failure has a total budget of $$600,000$

Product Testing has proposed to management a charge in the $2023$ budget for a new method of testing products.

It management decides to implement the new method, $$1\mathrm{.}50$ per unit of

appraisal cost will be saved, up to a level of $150,000$ tests. No additional savings are expected past the $150,000$ level. The new method involves $$95,000$ in training costs and $$65,000$ in yearly testing supplies.

Traditionally, $5\%$ of all completed items hove to be reworked. external failure costs average $$120$ per failed unit. The company$$s average external faillures are $1\%$ of units sold. The company carries no ending inventories.

Required:

a$.$ What is the adjusted budget for appraisal costs, assuming the new method is implemented and $800,000$ units are tested during the manufacturing process in $2023?$

b$.$ How much do internal failure costs change, assuming $500,000$ units are tested under the new method and it reduces the amount of unacceptable units in the manufacturing process by $40\%?$

c$.$ What would be the change in the external failure budget, assuming external failures are reduced by $60\%$ and the same facts as in part $($b$)?$