Question

2) Suppose an editor has been allotted $60000 to spend on the development and promotion of a new book. She estimates that if r thousand dollars are spent on development and y thousand dollars on promotion, approximately S(r,y)-20rly copies of the book will be sold. If she is allotted an extra $1,000 for development and promotion, how much should she expect the maximum sales level to change? 3) A consumer has $1120 to spend on two commodities, the first of which costs $7 per unit and the second $5 per unit. Suppose that the utility derived by the consumer from r units of the first commodity and y units of the second is given by U (r, y)- 130r0.2575. How many units of each commodity should the consumer buy to maximize utility?

Answer 1

2. yubyect to constaant + 60 2D D - Usvig Langaange maltiflrer mathod 20 x% =くし> 20 > マ9 S whane A is Lang range multilier YS= and 20~% く3oy, 202> =>(い) => 300 30x2 202 30t 20x =1.y+y=60 2-Sy =50 エ= 6o-24 = 36 = 24 3/2 103,680 Coblès a boak Sc36,24 20 (36 (24) Noo oha alloted $1000 exia for developmart and promotuis 1.St 1 2.5= 61 24.4 y24.4, = 61-24.4 = 36.6 108,0s4 Copies s(366,244) 20 (36.6 4.4= Maximum naler levdl change 108,054-103, 680 4,374 4.374 Capies oe book maxlmum nales arel changa 3. Lat xunits frot commodaity and y units afreacond Commnodity utih ty funchon Ucxsl 130 S Subedt to consaint 7x+5 = 1120 8cx)- Tメ+5y-1120 -O.TS 0.TS 0.25-0.25 マU =く32.5 x > ST.S I 9 2- <7, S> O.TS0.7 C32.5575 BA nA 0.25 y 37.Sx 32.s 750.75 4 97.5-5-05 > 7

O.7S 32.S x-7S 7 0.7S s (32.5) yo7s yas Subati ula th tha constant I=10ST.S)x = 4.2 SC32.5) 7x+SC4.2x) =1120 28x 1120 1120 28 -40 y=4.204)=168 Conxumor ohould buy fiyot omanodty 40 and aocond Comedty y 168 to maximize utilty