Return this evention to lits hilical statesBACKOAOUNDConsumer SurplusConsumer surplus (C.S.) is a measure of the benefit consumers gain when they are willing to pay more than the market price. For individual consumers, this is simply the difference between the amount the consumer is willing to pay minus the amount actually paid. Web respect to the market in question, it's found by calculating the area under the demand curve and above the market price. In other words, if D(x) is the demand eurve in a ghen matrit with equitilum point and E-(Q,p) then consumer surplus at equilibrium can be calculated as followe:C.S.=x=0Q(D(x)-p)dxor equivalentlyC*S:=x=0QD(x)dx-pQwhere x=0QD(x)dx will be referred to as the integral part of C.s. and pQ the revenue at equilibrium.Producer SurplusProducer surplus (R.S.) is a measure of the benefit producers gain when they are willing to supply an item for less than the market price. With respect to the market in question, it's found by calculating the area under the market price and above the supply ourve. In other words, if S(x) is the supply curve in a given market with equilibrium point and E=(Q.p) then producer surplus at equilibrium can be calculated as follows:P.S.=x=0Q(p-S(x))dxor equivalentlyP.S.=xQ=x=0QS(x)dxwhere x=0QS(x)dx will be referred to as the integral part of RS, and RQ the revenue at equilibrium.START QF PRORLIMSTART OF PROBLEMThe demand for cabin rentals in Chet Woods State Park is modeled by the function D(x), whereD(x)=1427-12.5xdollars per cabin per month, where a represents the number of cabins rented. The supply of the cabins is given byS(x)=10.1x251.8dollars per cabin per month. Again, a represents the number of cabins rented. checkbowes will display 5 different shaded regions (make sure jou consider them one at a time). Use the applet and the labels of the shaded regions to complete the problems below.(a) Find the equilibrium point and enter it as an ondered par Use the ceerdinates of the equilibrium point to complete the following.When supply and demand are at equitilum, there sall be cabins awalable at a rental price of 8 per month. This means that at equilitrium, the total monely revenue generated from cabin rentals will be $ This value of revenue corresponds to in the graph. Since the revenue is equal to this area, we can also compute the revence by finding the area. The area can be found by evaluating the definite integral below. plere we are only setting up the integral, not evaluating it). Revenue = Area -dx(b) Consider the formula for computing consumer surplus at market equilibrium. In this part, we will but compute the definite integral portion of the forms. See ce the definite integral from the consumer surplus formula below. Then, continue to fill in the blanks to perform the steps to evaluate the integral. Round the final answer to 2 decimal places. C.S. integral =dx=(roundto2 decimal places) The value of this definite integral corresponds to In the graph. (Keep in mind that the area chosen here is not the area that gives consumer surplus, because we have not yet finished the tormula].(c) Use your answers from parts (a) and (b) to calculate the consumer surplus when supply and demand are at equilibrium:Consumer surplus at equilibrium =Consumpar in/plis al equilbrium corresponds to in the graph.(d) Consider the formula for computing producer surplas at market equilierium, in this part, we will just compute the definite integral portion of the formula. Set up the definite integral from the producer surplus formula below. Thei, continue to fir in the blanks to perform the steps to evaluate the integral. Round the final answer to 2 declmal places.(round to 2 decimal places)The value of this definite integral corresponds to in the graph. (Keep in mind that the area chosen here is not the area that gives producer furplu, because we have not yet finished the formula).(e) Use your anwwe