a$)$ Let the demand function be $p=5-0\mathrm{.}5x$ and the supply function be $p=0\mathrm{.}25x.$ Find the equilibrium price and quantity.

b$)$ If a subsidy of Tk $5/4$ per unit is granted to the producer, find the new equilibrium price and quantity.

c$)$ Also find the total amount of subsidy granted in this case and the price per unit received with subsidy by the seller.