Answer to Question #220182 in Calculus for Ella

Question #220182

The demand equation for a particular kind of shirt is 2px+65p-4950=0, where x hundreds of shirts are demanded per week when dollars is the price of a shirt. Suppose that the shirt is selling this week at $30, and the price increases at the rate of $0.20 per week. Find the rate of change in demand. 


1
Expert's answer
2021-07-26T16:09:19-0400
2px+65p4950=02px+65p-4950=0

Differentiate both sides with respect to tt


2px+2px+65p=02p'x+2px'+65p'=0

Solve for xx'


x=p(2x+65)2px'=-\dfrac{p'(2x+65)}{2p}

Given p=30,p=0.20p=30, p'=0.20


2(30)x+65(30)4950=02(30)x+65(30)-4950=0

x=50x=50

Substitute


x=0.2(2(50)+65)2(30)=1.1x'=-\dfrac{0.2(2(50)+65)}{2(30)}=-1.1

 The rate of change in demand is 110-110 shirts per week.



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