Learning curve $($based on $2023$ exam$)$ Robotics company manufactures robots designed for healthcare applications. In February $2023$ the company wins a bid to produce $8$ robots of its newest model. The estimated production costs are as follows: $*$ Facility$-$related manufacturing overhead cost is allocated based on direct labor hour. $**$ Supporting overhead cost is allocated based on direct material cost. Robotics has an $\backslash (80\backslash \%\backslash )$ learning curve. And the company pricing policy is based on full production cost plus a mark up of $\backslash (35\backslash \%\backslash ).$ Required: a$)$ Calculate the following: i$)$ The selling price of the first robot manufactured. ii$)$ The prices of both the first and second robots manufactured if bought together. $(7$ marks$)$ iii$)$ The prices of the third and fourth robots manufactured if the first two have already been sold when the order is placed. $(9$ marks$)$ iv$)$ If all $8$ robots are sold to one customer what price would be charged per robot. $(9$ marks$)$ b$)$ Assume that the first $7$ robots have already been purchased by a customer. Another customer orders the $8$th robot. What would be the selling price of that $8$th robot? $($you should use the mathematical method to support your calculations, a $80\backslash \%$ learning curve means the learning coefficient, b $=\backslash (0\mathrm{.}321928)\backslash )(10$ marks$)(10$ marks$)$ Total: $40$ marks