A local group of scouts has been collecting aluminum cans for recycling. The gro

Question

A local group of scouts has been collecting aluminum cans for recycling. The group has already collected 13, 200 lb of cans, for which they could currently receive $5.64 per hundred pounds. The group can continue to collect cans at the rate of 400 lb per day. However, a glut in the aluminum market has caused the recycling company to announce that it will lower its price, starting immediately, by $0.12 per hundred pounds per day. The scouts can make only one trip to the recycling center. Find the best time for the trip. What total income will be received? Write the equation for the income, I, the scouts will receive in dollars after t days. I(t) =

Explanation / Answer

I(t)=(5.64)(132)+t(5.64-0.48t)

by doing dI/dt=0,we get t=5.875

As it is an increasing graph from t=5 to t=6 ,Income will be maximum at t=6 though there is t=5.875 which is not integer to consider.Hence Total income is 761.04 $

***Thank you

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