Question

A fruit grower estimates that if he harvests his crop of oranges now, he will get 100 pounds per tree, which he can sell for $.25 per pound. For each week he waits, he estimates that the crop will increase by 10 lb. per tree, but the price will decrease by $.01 per week. When should he pick the oranges to obtain the maximum profit? What would his profit be at this time?

Answer 1

Answer:

At 7.5 weeks will bethe best time

it will yield a profit of 30.63 per tree

Explanation:

we will construct the formula:

p = 0.25 -0.01w

q = 100 + 10w

Now, using SOLVER we can determinate the maximum profit point at 7.5 weeks

we construct these formula in excel, we stablish we can change only the "w" and it will look for the answer.

Now we can determinate the profit at this point:

P = 0.25 - 0.01 ( 7.5) = 0.175

Q =  100 x 10 (7.5) = 175

175 x 0.175 = 30.625 = 30.63