Question

A scout troop is collecting aluminum cans to raise money. They have collected 150 lbs. of aluminum for which they can get 80 cents per pound. If they continue to collect, they estimate they can get an additional 5 pounds of aluminum per day. The price of aluminum is decreasing 2 cents per day. If they can only make 1 trip to the recycling center, when should they make it? How much can they expect to collect for their cans? ( 5 days , $122.50 )

Answer 1

Since the price of aluminum is dropping at some point the extra 5 pounds you can collect per day does not give you more money and you should stop collecting. Let us find out how much money we will get for each extra day of collecting. Remember each day will give us 5 pounds more but the amount paid is 2 cents less per pound.

NOW: (150)(.80) = 120
1 day more of collecting: (155)(78)=120.90
2 days more (160)(76)=121.60
3 days more (165)(.74)=122.10
4 days more (170)(.72)=122.40
5 days more (175)(.70)=122.50
6 days more (180)(.68)=122.40

At 6 days more you see that the extra aluminum is not enough to make more money than the prior day because the price has dropped too much. This will continue. So, the best choice is to go 5 days more and make $122.50