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Let / (x] - 30h be the output quantity of a firm when the input is x. Suppose each unit of output is sold at a price of 30 euros. The cost function is C(x) = 15x ) Find the profit function m(x) and find the value of x 2 0 that maximizes profit 0 0 0 1 0 10 0 20 0 50 0 100 0 200 QUESTION 2 Is the profit function mix) convex (from Question 1)? O True O False O Indefinite QUESTION 3 Find the maximizer of the function y=x'ed. where a E [-1. 5]. A maximizer is a value of x that maximizes the function. 0 1 0 0 0102 03 04 05 QUESTION 4 Find the interval of concavity for the following function: f (x) = x + 4 O ( - 00. + 0) 0 (= 0. 0] 9 (- 0,0) @ ( - 0, 1) 0 ( -1. + 0 ) 0 [0, + co ) O (0. + 0 ) 0 (-1,1) QUESTION 5 Find the interval of convexity for the following function: / (x) = (+2)e-* O (- 00. + 00) 0 (- 00 .0] O (- 00 .0) 0 (-00 :1) 0 ( -1, + 0 ) O [0. + 0) 0 (0, + 0) 0(-1.1) QUESTION 6 The price a firm obtains for a commodity varies with demand Q according to the formula P(Q) = 18 - 0.006Q. Total cost is C(Q) = 0.00402 + 40 + 450 Find the firm's profit m(Q) and the value of Q* which maximizes profit. Choose the correct Q*. 0 0 O 100 0 500 9 700 0 1000 0 1100 O NA QUESTION 7 Find the maximum point of the function:/ (x) = 4--40x + 80 for x = [0.8] (Hint: you need to find a maximizer and then evaluate the function at that value)