Question 4 1 pt A farmer estimates that if he picks his corn

Question 4 1 pt A farmer estimates that if he picks his corn now his fields will yield 170 bushels per acre at a wholesale price of $4.2 per bushel. Each day he delays picking, he estimates his crop will increase by 3.8 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

Let t is the time from present

Volume of bushels at any time =170+3.8t

Price at any time =$(4.2-0.05t)

Total revenue =(170+3.8t)*(4.2-0.05t) =714+15.96t-8.5t-0.19t² =-0.19t² +7.46t +714

Let us take the first derivate of above equation w.r.t and keeping it equal to zero

dTCR/dt =-0.38t+7.46=0

t=19.63=20 days

so the answer is 20 days