Question

A company manufactures 2 models of MP3 players. Let x represent the number (in millions) of the first model made, and let y represent the number (in millions) of the second model made. The company's revenue can be modeled by the equation R(x, y) = 150x + 160y - 4x? - 3y? – ry Find the marginal revenue equations D Rz(x, y) = Ry(?, y) = We can achieve maximum revenue when both partial derivatives are equal to zero. Set R, = 0 and Ry = 0 and solve as a system of equations to the find the production levels that will maximize revenue. Revenue will be maximized when: XE ya

Answer 1

Date Page Sol" The am ampany's revenu is given by 1boy - 442-342 - my Riniy) - 150 nt than RA (ny) 22. Ry(0,0) 7? ! R g constant, Ry (n,y) represent to x contant Rala,y) represent the Rate of change of with respect to a keeping Similarly the rate of change of R with respect y keeping Rx (n,y) = a Ray) 150 x + 100g - 9x² - 3y2 - xy) x - ory 3x-y l Ja (1 150 to 8x – o Ralny) = 150 f Rylay 2 R (ay) प 2 (150 x + 16oy - q? - 3y2-ny) म 160 Ry (27) by-x

SID Page * Revenue will be maximum when Ralnim) & Ry (n.no CH 150-dn ay 20 4 160-64 HD solve alue for mig we have 8x60 we get 150 – 80 8 (160) -sary 150-fary -y-x) o 1280 t tha=0 +u8y 150 - 1280 t + try to - 1130 taty 4ry = 1130 ar y 1130 47 24.04 25 25 put y = 1130 IA wegeta 130 8u 47 ar 150 on - 1130 97

Date Page - 8 = 1130 47 -100 11 30 150x47 47 1130 7050 47 5920 $ x - 5920. 47x8 a 니ㅋ x = 15.7446 2 z = 105oon + 450 Assoy tlory - lona Z a the weekly of pounds of fire bol ata - 19 y ya 46 Z z losoo x lg tysuoxy6 t. loxig2x46 -lox 19 Igg500 + 207,000 t. 166060 - 68590 2 - 503,920 pounds

Date Page fod 2464) 2 Tn (1orron at 4500 4500g floxly - loa fu = losro & zoxy 3our at this fu losoo & 20 trony -3002 fy d (fmind) ry (lonront g eroy + lovly a lona) fy Grot 1042 Rate worker ie fa al tu slalled of charge of out pont wirt Lix y = is given by (B) answer fu 105oot 20x 19 x 46 30 x 192 = Tosvot 17u80 -10830 fu 17180 we weekly pounds per skalled woner

Date Page E Similarly = ?? at x 219, fy y =46 is 2 4500 tyox 19 fy 400 t 104 361 ugo t 3610 fy 8.110 محرم weekly pound per Unslecelled woolar