Samsung, a manufacturer and seller of television sets, operates through its assembly division $($AD$)$ and screen division $($SD$).$ The AD assembles TV sets using screens supplied by the SD$.$ Operating at full capacity, the SD incurs a cost of $$60$ for each screen it produces. These screens could be sold externally for $$105$ each, after accounting for $$10$ per screen in variable marketing and distribution costs. Conversely, if the AD opts to source screens from external suppliers at $$105$ each, it would face an additional variable purchasing cost of $$8$ per screen. In this scenario, managers of each Samsung division are empowered to maximize their division$$s operating income independently.

Please show all steps$/$calculations$/$explanations for credit

Tasks:

$1.$ Determine the minimum transfer price at which the SD manager would agree to sell screens to the AD$.$

$2.$ Identify the maximum transfer price the AD manager is willing to pay for screens from the SD$.$

$3.$ Considering a situation where the SD can only sell $80\%$ of its maximum capacity of $10,000$ screens per month on the open market, and the AD has the ability to assemble and market more than $10,000$ TV sets monthly:

a$.$ What would be the minimum transfer price for the SD manager to sell screens to AD$?$

b$.$ From the standpoint of Samsung$$s overall management, how much of the SD$$s production should be allocated to the AD$?$

C$.$ If Samsung's higher management directs the SD and AD managers to meet halfway between their respective minimum and maximum transfer prices, what would be the resultant transfer price? Would this price meet the objective outlined in the previous requirement $(3$b$)?$ Why or why not?