The supply function for a product is given by p = 20 + 100 radical 2x + 9, where

Wotzdorfg

Wotzdorfg

Answered question

2021-09-14

The supply function for a product is given by p = 20 + 100 radical 2x + 9, where x is the number of units supplied and p is the price in dollars. If the price is increasing at a rate of $1 per month, at what rate is the supply changing when x=20?

Answer & Explanation

Faiza Fuller

Faiza Fuller

Skilled2021-09-15Added 108 answers

Consider the given information,
p=20+1002x+9
x is the number of units supplied and p is the price in dollars
dpdt=$1
It is required to find the rate at which supply chaging at x=20
Differentiate the give supply function p with respect to ‘t’.
p=20+1002x+9
dpdt=100(122x+9(2dxdt))
dpdt=100(12x+9dxdt)
Now it is given that dpdt=$1
1=100(12x+9dxdt)
1100=12x+9dxdt
Put x=20
1100=12(20)+0dxdt
1100=17dxdt7100=dxdt
dxdt=0.07
Thus, rate at which supplying is chaging 0.07 units/month

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