Consider a market where supply and demand are given by QXS $=18+$ PX and QXd $=812$PX$.$ Suppose the government imposes a price floor of $$38,$ and agrees to purchase and discard any and all units consumers do not buy at the floor price of $$38$ per unit.

Instructions: Enter your responses rounded to the nearest penny $($two decimal places$).$

a$.$ Determine the cost to the government of buying firms$$ unsold units.

b$.$ Compute the lost social welfare $($deadweight loss$)$ that stems from the $$38$ price floor.