$4\mathrm{.}0/4\mathrm{.}0$ points $($graded$)$

Parts have already been partially processed before they reach a certain shop. When a part enters the shop, the company has

already spent $$10,000$ for both raw material and previous processing. More processing is required before they can be sold or

assembled onto a final product.

In that shop, machine $M$ takes one minute to do an operation. It costs $$500$ to do that operation. The machine is always

operational, but it has a probability $0\mathrm{.}1$ of creating a defective part. In other words, a part that is operated on by $M$ has

probability $0\mathrm{.}1$ of being unacceptable and probability $1-0\mathrm{.}1$ of being acceptable.

If the operation on it is good, the cost$-$based value of the part is $$10,000+$$$500.$ That is$,$ its value has increased by $$500.$ If the

operation is bad, the part must be scrapped and its market value is $0.($In that case, the company has lost $$10,500$ since it the

money spent on the operation was lost.$)$

What is the expected value of a part when it leaves the shop? $($This includes both good and bad parts.$)$

$9450$

What is the expected increase of a part's value due to the operation? $($It$\text{'}$s possible for this value to be negative$)$

$-550$

What is the production rate of good parts?Parts have already been partially processed before they reach a certain shop. When a part enters the shop, the company has already spent $$10,000$ for both raw material and previous processing. More processing is required before they can be sold or assembled onto a final product.

In that shop, machine M takes one minute to do an operation. It costs $$500$ to do that operation. The machine is always operational, but it has a probability $0\mathrm{.}1$ of creating a defective part. In other words, a part that is operated on by M has probability $0\mathrm{.}1$ of being unacceptable and probability $1-0\mathrm{.}1$ of being acceptable.

If the operation on it is good, the cost$-$based value of the part is $$10,000+$$$500.$ That is$,$ its value has increased by $$500.$ If the operation is bad, the part must be scrapped and its market value is $0.($In that case, the company has lost $$10,500$ since it the money spent on the operation was lost.$)$