A farmer estimates that if he picks his corn now his fields

A farmer estimates that if he picks his corn now his fields will yield 160 bushels per acre at a wholesale price of $4.4 per bushel. Each day he delays picking, he estimates his crop will increase by 3.9 bushels per acre, but the price will drop $0.05 per bushel. How many days should he delay picking to maximize the revenue he earns from his corn crop? Express your answer in days to the nearest whole day.

Solution

corn= 160 bushel per acre.

Wholesale price 4.4 bushel.

For 1 acre assume Corn-160 bushel, Revenue 160 X 4.4 = 704

Second day revenue 160+3.9 (4.4-0.5)

Let y day he picks.

R (Revenue Earned) = (160+3.9y) (4.4-0.5y)

=160x4.4-160X0.05y+3.9y X 4.4-3.9 X 0.05y²

=688-8y+15.91y-0.185y²

^{dr/dy= -8+15.91-2x0.185y2}

^{dr/dy=0 So, 7.91=2x0.185y, Y=21.37 days i.e 22 days.}