Question: a) Given the demand and supply functions for three interdependent commodities' Qm = 45_2PI +2132 2P3 Qm =16+2Pl P2+2P3 Q03 =30PI +2132 _P3 QS1=_5+2P1 Q52

a) Given the demand and supply functions for three interdependent commodities' Qm = 45_2PI +2132 2P3 Qm =16+2Pl P2+2P3 Q03 =30PI +2132 _P3 QS1=_5+2P1 Q52 =4+2P2 Q53 =_5+P3 Calculate the equilibrium prices and quantities of this three-commodity market model b) The demand function of a commodity is described by the experimental function P = 1058019 Where Q is the quantity demanded and TR = total revenue. Determine (i) The quantity for which the total revenue is maximized (ii) The maximum revenue dT R _ = 0 (Hint: revenue is maximized when 519 ) c) In making a certain item, a business has discovered that the demand function for the item is represented by 12:2 J; The cost function of producingx items is given by C = 0.5x + 500 (i) Find the price per unit that yields a maximum profit (1:) (ii) Find the output level that maximizes profit (iii) Find the maximum profit (1:) (iv) Show that the second-order condition has been fulfilled

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