Question: The willingness of toy manufacturers to supply a certain board game can be modeled as

\[S\left( p \right)=\left\{ \begin{aligned} & 0\,\,\,\,\,\text{thousand games}\,\,\,\,p<10 \\ & 20.43\left( {{1.07}^{p}} \right)\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,p\ge 10 \\ \end{aligned} \right.\]

where the games are sold in p dollars each.

(a) Find the price per game producers will accept if the market quantity is 50 thousand games

(b) Find the producer’s revenue if the market quantity is 50 thousand games.

(c) Find the producers’ surplus if the market quantity is 50 thousand games

(d) Find the amount producers are willing and able to receive if the market quantity is 50 thousand games