Problem $3.$

An automatic cookie machine must deposit a specified amount of $25+-0\mathrm{.}2$ grams $($g$)$ of dough for

each cookie on a conveyor belt. If the machine either over$-$ or underdeposits the mixtureby $0\mathrm{.}2$ grams,

it costs $$0\mathrm{.}02$ to scrap the defective cookie.

$($a$)$ Determine the Taguchi loss function?

$($b$)$ If the process is centered on the target specification with a standard deviation of $0\mathrm{.}06$ grams, what

is the expected loss per unit?

$($c$)$ If the process is normally distributed with a mean of $24$ grams and a standard deviation of $0\mathrm{.}06$

grams, what is the expected loss per unit?