Question

A boutique investment firm is in the business of producing high value deals for its clients. The production function for the firm takes on the following form:

Q= 3A²+4B²

A is the number of administrative assistants, and B is the number of investment bankers. The wage of an administrative assistant is $56,250 and the wage of an investment banker is $150,000. Each high value deal also requires $100,000 in infrastructure costs per deal. Determine the minimum cost of producing 76 high quality deals.

Answer 1

Lol The Given Production t 2 = 30 + 4B² - 0 The wage of administrative assistent 4-456,250 The wage of an Investment banker B= $ 150,000. Inforostaructor fractar coot of fer high Valle deal - $10,000 The Cost function ((x) = 56,250 A + 150,000 B The Lagrange function 2 = 56250 A + 150.000 B + M (Q-30² 618) - ③ foc dt OA 56250+ U L-6A) -0 — OL OB 15000ot 41-8B) = 0 OL Q-3 A² 4B² - 0 لال from ear 9 and 6 Au= 56250 (7 8Bl4 = 150000 C Now, eq" (7) dividing by eqh (8) 36 All By 56250 150000 1875 56250 х Goood 3750 А B В 4 A B 1875 3750 1 1 2

B=2A - Put the value of B from eah to ear ② 3n²+ 4 (2A)² = Q 30+ 16A²- Q 190 - 0 A 19 Put the value A and B in eqh (2) ((x) = 36250 56250 / + 150000 x 2 a 19 CO4) = 562509 + 3000 (4) SA 356250) The Cost of del High value deals 100,000 Q+(356250) The Cost of 76 High value deal = 100,000x76 + (3562.50) - 76,0 opco + 2x356250 - 7600000 +73500 Cost of the 76 High Valuce deal $153132 5 $8.312500