the component Question $2$ A technician in a quick oil change shop had the following service times $($in minutes$)$

for $12$ randomly selected cars:

a$)$ Please choose the suitable control charts to test whether or not the process is in

control.

b$)$ The specification for service time is between $4\mathrm{.}2$ minutes and $5\mathrm{.}2$ minutes, is the

specification being met? Using the formulation $=\frac{\sqrt[\phantom{2}]{n}}{3}\frac{A_2}{b}ar(R)(n$ is sample size and $A_2$

refers to tables below$)$ to estimate the standard deviation from average range.

Question $3$ The company plans to get a new machine to increase its capacity. There are two

machines can be selected: A and B$.$ The lifetime of machine A or B is $5$ years $($value decrease to

$0$ at the end of year $5).$ The cash flows are shown below:

a$)$ Based on the Average rate of return rule, which Machine should the company buy?

b$)$ Based on the net present value, which Machine should the company buy? $($Assume the $k$

is $4\%).$

For the $$100000$ investment, the company has two plans:

Plan A: use $$30000$ from the company and borrow $$70000$ from the bank to buy the

machine. The borrowed money will be paid annually back to the bank $($Equal loan

payment$)$ with an annual interest of $8\%$ in $5$ years. The maintenance is $$4000$ for each

year paid by the company.

Plan B: lease the machine from the supplier with an annual payment of $$26000$ for first

three years and purchase the machine at the end of year $3$ for $$40000.$ The maintenance

fee for the first three years is paid by the supplier and for the last two years is $$5000$

annually $($paid by the company$).$

The tax rate is $30\%$ and the depreciation is a straight line $($same amount every year$)$ and the

machine worth nothing to the company after year $5.$ The value decreases with a rate of $4\%$

$($k$)$ annually.

c$)$ For the buying options, how much should the company pay back to the bank each year?

And what is the tax saving for the year $2?$

d$)$ For the leasing options, what is the NPV for the year $2\text{'}$s activities?