Question

Suppose that the supply of x units of a product at price p dollars per unit is given by the following. p = 30 + 60 In(8x + 2) (a) Find the rate of change of supply price with respect to the number of units supplied. dp dx = (b) Find the rate of change of supply price when the number of units is 31. $ (c) Approximate the price increase associated with the number of units supplied changing from 31 to 32. $

Answer 1

c) Approximate the price increase associated with the number of unite supplied changing from 31 to 32. dp da bazu $ 1,92 -31 If in question asked exact valute, Exact value in the price increase associated with the number of units supplied changing from 31 to 32. Ple=32 - Pla=31 30 + 60 ln(8x32+2)] (30 +60 ln(8x3£ +2)) 11 60 en/8x32 +2 883) +2 $ 1.89 Plx=32 - Px=31

P = 30 +60 en ex+2) a) Rate of change of supply price with respect to the Number of unity supplied. do o+ 60 x I (84+2) x 8 dx 480 de da 240 42+1 8x +2 de da 240 = Anywer 4xti Rate of change of supply price when 31 units De = 240 de dhe 240 4x31+1 240 125 x = 31 124 +1 dp dre bacz $ 1.92 Answer x=31 C ) Plaxese Pla=3,= 30 +60 ln (8 x 32 +2)7- 30 +60 ln (8x31+2)] Go in (8x377) $ 1.89 - Plx=32 - Plx Plx=31 Answer