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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Question:

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).Givenp = $7q = 800 Requireddq/dpDifferentiating the function implicitly with respect to p shown;2p + 400d dq/dp = 0400q dq/dp = -2p200qdq/dp = -pdq/dp = -p/100qsubstitute p and q into the resulting equation;dq/dp = -7/100(800)dq/dp = -7/80000dq/dp = -0.0000875This means that the rate of change of quantity demanded with respect to the price is  -0.0000875

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