Division Y has asked Division X of the same company to supply it with 8,800 units of part L763 this year to use in one of its products. Division Y has received a bid from an outside supplier for the parts at a price of $52 per unit. Division X has the capacity to produce 35,200 units of part L763 per year. Division X expects to sell 31,680 units of part L763 to outside customers this year at a price of $56.80 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 L763 at a variable cost of $44 per unit. The cost of packing and shipping the parts for outside customers is $2 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 8,800 parts this year from Division X to Division Y? (Round your final answers to 2 decimal places.)b. Is it in the best interests of the overall company for this transfer to take place?

a. From the perspective of Division X, profits would increase as a result of the transfer if and only if:Transfer price > Variable cost + Opportunity costThe opportunity cost is the contribution margin on the lost sales, divided by the number of units transferred:Opportunity cost = [(${{[a(5)]:#,###.00}} − ${{[a(6)]:#,###}} − ${{[a(7)]:#,###}}) × {{[a(10)]:#,###}}*] / {{[a(1)]:#,###}} = ${{[a(8)]:#,###.00}}
Therefore, Transfer price > ${{[a(6)]:#,###}} + ${{[a(8)]:#,###.00}} = ${{[a(11)]:#,###.00}}.From the viewpoint of Division Y, the transfer price must be less than the cost of buying the units from the outside supplier. Therefore,Transfer price < ${{[a(2)]:#,###.00}}.Combining the two requirements, we get the following range of transfer prices:${{[a(11)]:#,###.00}} < Transfer price < ${{[a(12)]:#,###.00}}.b. Yes, the transfer should take place. From the viewpoint of the entire company, the cost of transferring the units within the company is ${{[a(11)]:#,###.00}}, but the cost of purchasing them from the outside supplier is ${{[a(12)]:#,###.00}}. Therefore, the company's profits increase on average by ${{[a(13)]:#,###.00}} for each of the special parts that is transferred within the company.