A$.$ Is there a bottleneck $($constraint$)?$ If so$,$ which resource is a bottleneck $($constraint$)?(5$

points$)$

B$.$ Determine the product mix $($type of cookie and how many boxes for each type$)$ that

would maximize the profit. $(5$ points$)$

C$.$ Calculate the profit. $(2$ points$)$

$2.$ A process filling small bottles with baby formula has a target of $3$ ounces $\{0\mathrm{.}150$ ounce.

Two hundred bottles from the process were sampled. The results showed the average

amount of formula placed in the bottles to be $3\mathrm{.}042$ ounces. The standard deviation of the

amounts was $0\mathrm{.}034$ ounce. Is this process capable? $(1$ point$)$ Justify your answer with

process capability calculations? $(3$ points$)$

$3.$ Aspen Plastics produces plastic bottles to customer order. The quality inspector randomly

selects samples of bottles from the bottle machine and measures the outside diameter of

the bottle$-$cap, a critical quality dimension that determines whether the bottle cap will fit

properly. The mean diameter $($in inches$)$ of the sample obtained from the machine$$s

production output is $0\mathrm{.}592.$ The process standard deviation is $0\mathrm{.}01.$ Suppose that the

specification for the bottle$-$cap diameter is $0\mathrm{.}600\backslash$pm $0\mathrm{.}050.$ What is the process capability

index for this process? $(2$ points$)$ If the firm is seeking four$-$sigma performance, is the

process capable of producing the bottle? $(2$ points$)$