Can you solve these questions with full explanation

A rm called Shanghai Housing Limited has won a tender to build housing units within the Durham city council. As part of its initial planning, it found out that the demand and supply functions for houses in Durham are given by the following: P5 = B+BQs and Qd|= ctPd a) Represent the above functions on a suitable graph, properly labeling all the axes and curves. b) Find the equilibrium values of quantity and price. c} l_n__o_rdgr_t_o increase housing units, Durham local council is thinking to offer a subsidy of k per housing unit. Discuss, using postsubsidy expressions, the possible effects on equilibrium house prices and quantities if this decision is implemented d) Write expressions for the price elasticities of demand and supply of housing after the granting of the subsidy. e] Write appropriate expression showing the projected total expenditure of Durham count! council that is related to the subsidy. Information available to Shanghai Housing Limited also indicated that the total variable cost for such a project is given by: TVC(C1) = 8Q2 + \"Q Where Q is quantity of housing units produced and 5 and are positive constants. You also know that the total costs i=5 approximated to be El if no housing units are produced. f [9 Using appropriate equations, write the estimated housing profit function for this firm. f(ii) Using your information from H!) or otherwise, work out an expression for the number of housing quantity that will maximize profit