Question

Suppose that the wholesale price of a certain brand of medium-sized eggs, ? (in dollars per carton,) is related to the weekly supply ?, (in thousands of cartons,) by the equation 625?^2 − ?^2 = 100 If 25,000 cartons of eggs are available at the beginning of a certain week and the price is falling at a rate of $0.04/caton/week, at what rate is the weekly supply changing? Answer in a complete sentence using the context of this problem and appropriate units, rounding to the nearest whole unit. Indicate if the supply price is increasing or decreasing.

Answer 1

The given demand function is,

diff wrt t,

plugin the values,

multiply by 1000,

rounding off to whole unit,

The -ve sign indicates that the supply price is decreasing.

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