v$.$ The Mad Hatter is a Vancouver manufacturer of hats. In March the company received an order to produce $800$ specialty hats to be worn during the opening ceremonies of the winter Olympics. The Mad Hatter estimates that $100$ of these hats can be produced in a total of $25$ direct labour hours. Costs associated with this order are, direct materials at $$12$ per hat, direct labour at $$25$ per hour, variable manufacturing overhead at $$5$ per direct labour hour, and fixed manufacturing overhead of $$8,000.$ The company expects an $80\%$ learning curve. The Index of Learning $=-\mathrm{.}3219$

Required:

Without the learning curve, how many direct labour hours will it take to manufacture the hats?

Using the cumulative average time learning model, how many direct labour hours will it take to manufacture the hats?

Using the incremental unit time learning model, how many direct labour hours will it take to manufacture the hats?

If The Mad Hatter plans to set the selling price for the new hat at $200\%$ of production costs, what would be the selling price per hat under both learning curve models?