Question

Company produces 2 products Π₁ and Π₂, with a joint function of total cost TC=40Q₁+4Q₁Q₂+40Q₂ and a joint function of total revenue TR=200Q₁-4Q²₁+12Q₁Q₂+120Q₂-2Q²₂, where Q₁ and Q₂ are the quantities of Π₁ and Π₂ respectively.

1) Find the maximum profit if the company has a production contract of 60 units in total.

2) Αpproximate the new maximum profit if total output increases by one unit.

Answer 1

TR = 2000,-402 +120,02 +12002 - 207 Page 1 TC = 900, + 40,02 + 4002 Joint porfit (11) - TR - TO a = 2000,- 40,2 +120,02 +12002 – 202-400,-40,02-4002 TI = 1600, -40,+80,02 + 8002-20 Foc : 36 = 0 & 294 0 zuen = 0 => 160 -80, +802 = 0 = 80,-802-160 = 0, - Q2 =20 – = 80, +80 -4Q2 = 0 => 402 – 80, = 80 » Q2-20, = 20 —

Total = 60 Page 2 0,+ 02 - 60 02 = 60 -, - Put ean. in ean. O O, - 0,20 Q, - (60-0,) = 20 Q, -60+Q,- 20 →20, = 80 0,- 40 O2 = 60-0, 1 = 60-40 | 0y = 20 at Q, = 40 & Qy = 20, TR = 2oo( vo) - 4 (40) + 2( )(2) + (2 0 (20)- 2(20) = 8000 – 6400+ 9600 + 2400-800 = 20,000 – 7,200 = 12,800 TC = 40(40) + 4(40)(20) + 40(20) 1600 + 3200+800 = 5600 Maximum Profit - TR-TC = 12,800 -5,600 = $ 7200 Ans 2 Now, Q = 61 Q, +Q, = 61 O2 = 61-Q, - Put ear. @ in ean. ☺ ©

(20.5)^ @,-02-20 Page 3 Q, - (61-0,) = 20 20, = 20 +61 a, = 40.5) Qg = 61-01 = 61-40.5 Q2 = 20.5 at Q, = 40.5 & On = 20.5; TR = 20 ( 40.5) -4 (4 p.52+12 (ực. (20.52+12 (20.5)- = 8100 - 6561 + 9963+ 2460 - 840,5 = 20,523 – 7,401.5 = 13,121.5 Te = 40(40.5) +4(40.5)(2015) + 40/20,5) = 1620 + 3321+ 820 = 576) | Maximum Ph} : TR-TC = 13,121.5 – 5,761 = $ 7,360.5 Ary

**if you liked the answer, then please upvote. Would be motivating for me. Thanks!