It takes an operator $0\mathrm{.}038$ h to load a machine and $0\mathrm{.}015$ h to walk to the next machine. Each machine runs automatically for $0\mathrm{.}164$ h$.$ With an operator rate of $$12\mathrm{.}80/$h and a machine rate of $$14/$h$,$ calculate the following:

Enter answer in the textboxes below. Enter only numerical values in the text boxes and round to $2$ decimal places. Attach spreadsheet showing your complete work in the file response question ie$.$ question #$4.$

a$)$ The optimum number of machines the operator can be assigned $($round to $2$ decimal places$)[$Opt$]$

b$)$ The total expected cost in dollars per unit of production for one machine when the operated is assigned the optimum number of machines rounded down.$[$TECDOWN$]$

c$)$ The total expected cost in dollars per unit of production for one machine when the operated is assigned the optimum number of machines rounded up$.[$TECUP$]$

d$)$ What is the preferred number of machines per operator