$1.$ Twenty$-$five engine mounts are sampled daily and found to have an average width of $2$ inches,

with a standard deviation of $0\mathrm{.}1$ inches. What are the control limits that include $90\%$ of the sample means? $(2$pts$)$

$\_\_\_2.$ Cans of Soda are sampled to ensure proper weight. The overall average for the sample is $10$ ounces.

Each sample contains $25$ cans. The standard deviation is estimated to be $3$ ounces. What are the $98\%$ control limits$?$

$\_\_3.$ LEE$$s Distributors, Inc. at Glassboro fills catalog orders. Samples of size n $=100$ orders have been taken each

day over the past $6$ weeks. The average defect rate was $0\mathrm{.}05.$ What are the upper and lower limits for the process

for $99\mathrm{.}73\%$ confidence?

$*$

$(4-5)$ A Glassboro township is concerned about adverse public reaction to a trash recycling project that is currently in progress. Because of this, the commissioner of public works has authorized a weekly survey of township residents to be constructed. Each week, $100$ residents are questioned on their feelings toward the project. The results to date are shown below. Answer using an appropriate control chart.

Weeks:

$1$

$2$

$3$

$4$

$5$

$6$

$7$

$8$

No$.$ of opposed:

$3$

$4$

$4$

$3$

$3$

$7$

$3$

$3=30$ total

$4.$ What is the weekly average proportion of opposed feelings?

$5.$ What are the $95\%$ control limits$?$

$*$

$(6-7)$ A construction foreman has three earth$-$moving machines that Machine can be operated by workers

Machine A$,$ B$,$ C$,$ and D at costs$/$hours$.($in $$)$ as designed in the matrix shown.

$1234$ Find the least cost allocation of workers to machines $1,2,3,$ and $4.$

A $8624$

Job B $671110$

C $3576$

D $510129$

$6.$ To which machine would you like to assign Job C$?$

$7.$ The minimum total cost after assigning jobs to machines is $(4$ pts$)$: