Question

A commercial cherry grower estimates from past records that if 25 trees are planted per acre, then each tree will yield an average of 37 pounds of cherries per season. If, for each additional tree planted per acre (up to 22), the average yield per trae is reduced by 1 pound, how many trees should be planted per acre to obtain the maximum yield per acre? What is the maximum yield? pounds, trees should be planted per In order to get the highest yield of acre.

Answer 1

1.
Total yield=(25+x)*(37-x)
=25*37+12x-x^2
Maximization occurs at 12-2x=0
=>x=6

So, Highest yield of (25+6)*(37-6)=961 pounds, 31 trees should be planted per acre

2.
Area=lb=1800
Cost of fencing=(2l+b)*4+b*12=(2l+1800/l)*4+1800/l*12=8l+28800/l
Maximization occurs at 8-28800/l^2=0
=>l=(28800/8)^(1/2)=60.00
b=1800/60=30.00

The ahort side is 30 ft. and the long side is 60 ft.