Question

Question 4 1 pts 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 3.1 bushels per acre, but the price will drop $O.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.

Answer 1

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+3.1 (4.4-0.5)

Let y day he picks.

R (Revenue Earned) = (160+3.1y) (4.4-0.5y)

=160x4.4-160X0.05y+3.1y X 4.4-3.1 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.}