Homework SourseA company selling widgets has found that the number of items
A company selling widgets has found that the number of items sold, x, depends upon the price, p at which they\'re sold, according the equation x=(80000)/((0.2p+1)^2)
Due to inflation and increasing health benefit costs, the company has been increasing the price by $0.05 per month. Find the rate at which revenue is changing when the company is selling widgets at $8 each.
Revenue is decreasing by ____ dollars per month?
(Answer should be positive)
Due to inflation and increasing health benefit costs, the company has been increasing the price by $0.05 per month. Find the rate at which revenue is changing when the company is selling widgets at $8 each.
Revenue is decreasing by ____ dollars per month?
(Answer should be positive)
Solution
x=(80000)/((0.2p+1)^2)
dx/dp = (-32000)/(0.2p + 1)^3
dp/dt = 0.05
dx/dt = (dx/dp)(dp/dt) = (0.05)(-32000)/(0.2p + 1)^3
dx/dt when p = 8 -----> -91.033
Revenue is decreasing by 91.033 dollars per month
