Carver Pump Company is making specialty pumps for an outdoor fountain. The company has built $5$ prototype pumps and recorded the direct labor $($in minutes$)$ for each pump as follows:

$1$: $500$

$2$: $475$

$3$: $461$

$4$: $451\mathrm{.}3$

$5$: $443\mathrm{.}9$

The company prices their pumps at $$300$ per direct labor hour. They have found that this pricing scheme covers labor, material and overhead costs and provides for a suitable profit. Using learning curve theory, how much should the company charge for $40$ pumps, assuming that they can use the $5$ prototype pumps in completing the order.

Question $2$ options:

$$98,051$

$$4,902,568$

$$81,709$

$$1,903$

$$114,166$