$1.(\backslash (\backslash$mathbf$\{20\}\backslash )$ points$)$ You run a local electronics store, and a company has contracted you to sell them $25$ rovers that can climb stairs. They are asking for very specific sensors$,$ so you will need to assemble each rover separately. From past experience you know that assembling a new configuration of a rover takes $3$ hours. You budget $\backslash (\backslash$$ $60\backslash )$ per hour of your time and the parts going into each rover cost $\backslash (\backslash$$ $250\backslash ).$ Your learning rate for a mechanical task is $\backslash (80\backslash \%\backslash ).$ a$.$ Assuming your learning rate remains constant, how long will it take to assemble the $\backslash (25^\{\backslash$text $\{$th $\}\}\backslash )$ rover? b$.$ What is the average assembly time for the $25$ rovers? Assume that the approximation formula is valid. c$.$ How much would you charge the company if you wanted to get $\backslash (\backslash$$ $750\backslash )$ profit from this contract? Assume that all overhead is included in the $\backslash (\backslash$$ $60\backslash )$ per hour rate. d$.$ How much should you charge, if you assume that you cannot assemble a rover in less than $1\mathrm{.}5$ hours? In other words, the effect of learning stops at some point.