$2\mathrm{.}8.$ A company wants to develop a level production plan for a family of products. The open$-$ ing inventory is $550$ units, and a decrease to $200$ units is expected by the end of the plan. The demand for each of the periods is given in what follows. All periods have the same number of working days. How much should the company produce each period? What will be the ending inventories in each period? Do you see any problems with the plan?

Period $123456$ Total

Forecast demand $130012008006008009005600$

Planned production

Planned inventory $550$Consider the product structure tree shown below:

With a beginning inventory of fifteen for all components on level one, twenty for all components on level two, and zero for all components on level three and finished items, how many of each component on level three are needed to produce $20$ product X$\text{'}$s$?$QUESTION $4[$CLO $1]$

A$).$ A rendering plant wishes to use the data $($sales records from a few local businesses and the month

of the year$)$ to help determine their supply level for the coming months. The records shown in the

table provide an excellent opportunity for you to assist them with their forecasting.

Month Sales Pounds

January $4554\mathrm{.}3$

February $5763\mathrm{.}8$

March $3239\mathrm{.}5$

April $4449\mathrm{.}8$

May $5152\mathrm{.}3$

June $3439\mathrm{.}9$

i$)$ What is the regression equation resulting from using Sales to forecast Pounds? $(3$ marks$)$

ii$)$ What is the regression equation resulting from using the month, where January $=1,$ February $=2,$

etc.$)$ to forecast Pounds? $(3$ marks$)$

iii$)$ What are the salient performance statistics for the simple regression of Pounds on Sales?

Provide an interpretation. $(4$ marks$)$