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REQUIRED: Solve the following: a) A rm's inverse demand function is 30 = 35 P and the average cost function is 36 AC 3 + 8 At what quantities does the rm make a prot of $24? b) Suppose the future circulation of the newspaper is given by the equation, N = c(1 3"\") I where N is the daily circulation after t days of publication and r: and k are positive constants. (i) make It the subject of the formula (ii) Using the expression derived in question b(i). evaluate the following: If c = 740000 and k = 0.025, after how many days will the daily circulation reach 525000? c) A manufacturer's marginal cost (MC) function is given by: Find the equation of the total cost function if total costs are 5200 when Q = 8. d) A population of size x is decreasing according to the law dx x dt 250 where t denotes the time in days. If initially the population is of size are, nd how long it takes for the size of the population to be halved