The Poisonwood and Prodigal Divisions are part of the same company. Currently the Prodigal Division buys a part from Poisonwood for $$82.$ The Poisonwood Division wants to increase the price of the part it sells to Prodigal to $$100,$ which is the price it charges customers outside the group. The cost data for the Poisonwood Division is as follows:Direct materials $$25\mathrm{.}50$Direct labor $$32\mathrm{.}50$Variable overhead $$22\mathrm{.}50$Fixed overhead $$9\mathrm{.}60$ Required:Explain and calculate the transfer prices at which Poisonwood Division should offer to transfer the part to Prodigal Division in order that the group profit maximizing decisions may be taken on financial grounds in each of the following independent situations: $($a$)$ Poisonwood Division has an external market for its entire product. $($b$)$ Poisonwood Division has excess capacity to supply all parts needed by the Prodigal Division. $($c$)$ Poisonwood Division has excess capacity for only $3,000$ of the total $10,000$ parts needed by the Prodigal Division. However, the Poisonwood Division has an alternative use of this excess capacity which equates to a contribution of $$5$ for each part.