An fruit grower knows from previous experience and careful d

An fruit grower knows from previous experience and careful data analysis that if the fruit on a specific kind of tree is harvested at this time of year, each tree will yield, on average, 140 pounds, and will sell for S3.8 per pound. However, for each additional week the harvest is delayed (up to a point), the yield per tree will increase by 2 pounds, while the price per pound will decrease by S0.05 A) How many weeks should the grower wait before harvesting the apples in order to maximize the sales revenue per tree? (Round your answer to the nearest tenth of a week.) Answer B) Use your answer in part A to find the actual maximum revenue that can be expected. (Round your answer to the nearest dollar.) Answer: (rounded to the nearest tenth) dollars (rounded to the nearest dollar)

Solution

revenue = ( 140 + 2x ) ( 3.8 - 0.05 x)

so the function becomes

R(x) = -0.1x^2 +0.6x + 532

maximum revenue occurs at

x = -0.6 / 2(-0.1)

x = 3

so , grower must wait for 3 weeks in order to maximize profit

b) maximum profit is  -0.1(3)^2 +0.6(3)+ 532

maximum profit = $ 533