No detail calculate is also ok prefer handwriting

2. A car manufacturer produces sedans and hatchbacks. Its demand and total cost functions are given as follows: Q1 = 60 - 0.5 P, Q2 = 100 - P2 TC = Q2 + Q2 + 4Q, Q2 where Q1 and Q2 represent the quantities of sedans and hatchbacks, respectively. P, represents the price of a sedan (in thousands) and P2 represents the price of a hatchback (in thousands). (a) Find the inverse demand functions for sedans and hatchbacks and determine the manufacturer's total revenue function. [3 marks] (b) Find the expression for the car manufacturer's profit function. [2 marks ] (c) Use partial differentiation to calculate how many sedans and hatchbacks the manufacturer should produce to maximise the profit. Show that the profit is a maximum using second-order conditions. [10 marks] (d) Compare the price elasticities of demand for sedans and hatchbacks when profit is maximised. Which product is more price sensitive? [5 marks] 3. (a) In a report submitted to the management of PostAway. Miss Jules, the Logistics Manager reports that her team experienced 5 delivery failures during the last 50 days. robability distribution would Dest to use he Five reasons to [3 marks] ii. Find the probability that there will be 5 or more delivery failures in a 50- day period. [7 marks] (b) Bob is buying two fighter fish from a pet shop. The shop's tank contains seven male fish and six female fish but they all look the same. Find the probability that Bob's fish are i. both the same sex [2 marks] ii. both female [1 mark] iii. both female given that they are of the same sex. [2 marks]