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A nightclub has approximated the demand for their Thursday night drink special by p^2+200q^2=177​, where p is the price​ (in dollars) and q is the quantity demanded​ (in thousands). Find and interpret when the price is ​$ 7 and the demand is 800 drinks.

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Answer:

Step-by-step explanation:

Given the approximate demand function of night drink expressed as;

p^2+200q^2=177​,

p is the price​ (in dollars) and;

q is the quantity demanded​ (in thousands).

Given

p = $7

q = 800

Required

dq/dp

Differentiating the function implicitly with respect to p shown;

2p + 400d dq/dp = 0

400q dq/dp = -2p

200qdq/dp = -p

dq/dp = -p/100q

substitute p and q into the resulting equation;

dq/dp = -7/100(800)

dq/dp = -7/80000

dq/dp = -0.0000875

This means that the rate of change of quantity demanded with respect to the price is  -0.0000875

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