Question

Q5. Suppose a store wishes to sell shirts whose respective demand function and cost functions are given as P=120-5Q and TC =60+20 Q. (i) Write down the equations for TR and Profit (r.. (1 mark) (ii) Graph the TR and TC functions with TR and TC on the vertical axis and Q on the horizontal. (2 marks)

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Answer 1

TR 1Roch- 503 Solution Given ; Pa 120 - 50 TC = 60+ 200 Total revenue = (180-58) a And, Profit - TR-TC =(180Q -50%)-(50 +200) profit a 100 Q - 50²-60 3504 300+ 2507 200 ТС 150 100 Ř Š ý Ś 4 -3 -2 .1 O 0.61

i) To maximize profit (Profit) = d (100 Q - 502-60) = 0 da =) 100 - 100 - a = 10 So, Maximum profit when Q=10 Profit (0-10) = 100 (10)-5(10)²-60 21000 - 500 - 60 440 But if a=g then profit - 100 100(9)-5(9)2-60 = 435 and if Q=11 then, Profit 100 (11) - 5 (1192-60 435 Profit is maximum when Q = 10 Hence,