Division $\backslash ($ Y $\backslash )$ has asked Division $\backslash ($ X $\backslash )$ of the same company to supply it with $5,400$ units of part L$763$ this year to use in one of its products. Division $\backslash ($ Y $\backslash )$ has received a bid from an outside supplier for the parts at a price of $\backslash (\backslash$$ $35\backslash )$ per unit. Division $\backslash ($ X $\backslash )$ has the capacity to produce $21,600$ units of part L$763$ per year. Division $\backslash ($ X $\backslash )$ expects to sell $19,440$ units of part L$763$ to outside customers this year at a price of $\backslash (\backslash$$ $36\mathrm{.}40\backslash )$ per unit. To fill the order from Division Y$,$ Division X would have to cut back its sales to outside customers. Division X produces part L$763$ at a variable cost of $\backslash (\backslash$$ $27\backslash )$ per unit. The cost of packing and shipping the parts for outside customers is $\backslash (\backslash$$ $2\backslash )$ per unit. These packing and shipping costs would not have to be incurred on sales of the parts to Division Y$.$

Required:

a$.$ What is the range of transfer prices within which both the Divisions' profits would increase as a result of agreeing to the transfer of $5,400$ parts this year from Division $\backslash ($ X $\backslash )$ to Division Y$?($Round your final answers to $\backslash (\backslash$mathbf$\{2\}\backslash )$ decimal places.$)$

Range of transfer prices:

$$ Transfer price $$

b$.$ Is it in the best interests of the overall company for this transfer to take place?

Yes

No