$7.$ Short answer and multiple choice $($clearly show the correct answer$).$

The first two questions involve the project below with $5$ activities.

Activity Length Predecessor

A $7-$

B $4-$

C $4$ A

D $5$ A$,$B

E $5$ C

$7\mathrm{.}1$ Draw the network below.

$7\mathrm{.}2$ How many ending activities are there?

a$)1.$

b$)2.$

c$)3.$

d$)4.$

The following two questions involve a service process that has a mean of $88$ seconds with a standard deviation of $5$ seconds, where the upper and lower specification limits for the process are $100$ seconds and $76$ seconds, respectively.

$7\mathrm{.}3$ What is the process capability ratio for this process?

a$)0\mathrm{.}667$

b$)0\mathrm{.}80$

c$)1\mathrm{.}25$

d$)3\mathrm{.}00$

e$)17\mathrm{.}6$

f$)$ none of these.

$7\mathrm{.}4$ Is this process capable of providing an acceptable level of quality $(99\mathrm{.}7\%$ acceptable$)?$

a$)$ yes.

b$)$ no$.$

$$

$7\mathrm{.}5$ The purpose of a control charts is to identify when a process has

a$)$ random variation.

b$)$ non$-$random variation.

$7\mathrm{.}6$ There are two options for producing a product, A and B$.$ Option A has a higher fixed cost than Option B$,$ but a lower variable cost. If the variable cost of Option A was increased, then the level of production that causes both options to have the same total cost would

a$)$ increase.

b$)$ decrease.

c$)$ stay the same.

$7\mathrm{.}7$ The project shown below includes $10$ activities $($represented by the circles$)$ with precedence relations as shown by the arrows. Activity times are not shown. What is the fewest number of activities that could be in the critical path?

a$)1.$

b$)2.$

c$)3.$

d$)4.$

e$)$ none of the above.

$7\mathrm{.}8$Crashing$$ a project is used to

a$)$ lengthen the time to complete a project.

b$)$ shorten the time to complete a project.

c$)$ find the earliest start and latest start of a project.

d$)$ find the latest start and latest finish of a project.

$7\mathrm{.}9$ There is a $20\%$ chance the outcome is a gain of $$2000$ and an $80\%$ chance the outcome is a loss of $$500.$ What is the expected value of the outcome?

a$)$ $$1500.$

b$)$ $$800.$

c$)$ $$500$

d$)$ $$0$

e$)$ none of the above.

$7\mathrm{.}10$ For a control chart, what percentage of points are expected to be between the upper and lower control limits$?$

a$)50\%.$

b$)90\%.$

c$)96\mathrm{.}7\%$

d$)99\mathrm{.}7\%$

e$)99\mathrm{.}99\%$

f$)$ none of the above