For this week's assignment, you are tasked to display your problem$-$solving skills. Work on the following problems and submit a document with all the answers completed. You MUST show the step$-$by$-$step work for solving the problems.

Problem $1$

Cynthia's Design Studios had sales in the last four months of $$13,700,$$$15,400,$$$17,100,$ and $$18,800.$ Sales are related to how many designers Cynthia has on duty. The sales forecast helps her decide on the proper staffing levels.

a$.$ What is the forecast for the fifth month using a two$-$period moving average?

b$.$ What is the forecast for the fifth month using $=0\mathrm{.}9$ in an exponential smoothing model with $A_4=$$$18,800$ and $F_4=$ $$16,913$ to get things started.

Problem $2$

Currently, the manufacturer has eight machines that operate on a two$-$shift $($eight hours each$)$ basis. Twenty days per year are available for scheduled maintenance of equipment. Assume there are $250$ workdays in a year. Each manufactured good takes $26$ minutes to produce.

a$.$ What is the effective capacity of the factory?

b$.$ Given the five$-$year forecast, how much extra capacity is needed each year?

c$.$ Does the firm need to buy more machines? If so$,$ how many and when?