Carmaker produces small cars. As production emits pollution, Carmaker needs to buy pollution permits. It also needs to hire labour. Carmaker's production function is given by: (1) q = min{0.05L, E1/2}, where E denotes the number of pollution permits, L denotes the amount of labour and min{a,b} denotes the minimum function where min{a,b} = a if a b and min {a,b} = b if a b. (a) [1 mark] Draw the isoquant corresponding to q = 10 in a clearly labelled diagram where L is in the x-axis and E is in the y-axis. Label two pairs of E and L in the diagram which give q = 10. (b) [2 marks] What is the marginal product of L and the marginal product of E when L = 40 and E = 100? Does the production function (1) exhibit constant returns to scale for all L > O and E > 0. (c) [1 mark] Let m denote the price of a pollution permit and w denote the price of labour. Find the minimum cost to produce q cars when w = 200 and m = 20. [Hint: the answer would involve q.]