Question

A company selling widgets has found that the number of items sold
x depends upon the price pat which they're sold, according the equation
x=80000√2p+1 .

Due to inflation and increasing health benefit costs, the company has been increasing the price by $3 per month. Find the rate at which revenue is changing when the company is selling widgets at $210 each.

dollars per month

Answer 1

revenue r(x) = quantity * price = x * p
Assuming the usual carelessness with parentheses, I get
r = 80000p√(2p+1)
dr/dt = 80000 * (3p+1)/√(2p+1) dp/dt
so plug in your numbers to ger
dr/dt = 80000 631/√421 * 3 ≈ $7.38M/mo

Answer 2

This is far from the right answer. The correct answer is 5862.33

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