The owner of an orange grove must decide when to pick one variety of oranges. She can sell them for $27 a bushel if she sells them now, with each tree yielding an average of 7 bushels. The yield increases by half a bushel per week for the next 5 weeks, but the price per bushel decreases by $1.50 per bushel each week. In how many weeks should the oranges be picked for maximum return?

The oranges should be picked in 2 weeks for maximum return

Explanation:

We assume that the return of the owner is y ($)

Assume that the number of weeks the oranges should be picked to have maximum return is x (weeks). (x≥0)

If collect now, the price for each bushel is $27

As the price per bushel decrease by $1.50 per bushel each week

=> After x weeks, the price of a bushel decrease: 1.5x ($)

=> The price of 1 bushel after x weeks is: 27 - 1.5x ($)

If collect now, each tree can yield 7 bushels

As the yield increases by half a bushel per week for the next 5 weeks

=> After x weeks with x ≤ 5, each trees would yields: 7 + 0.5x (bushels)

The return = The price of each bushes × The quantity of bushels

=>

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We have: if the equation has the form of with a≠0, its maximum value is:

In the equation , we have: a = -0.75; b = 3; c = 189

=>

To look for the number of weeks, we should find x (0≤x≤5) with which y = 192

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⇔ x = 2

The oranges should be picked in 2 weeks for maximum return

answer; (d) i believe that the correct answer is ; /// a new invention lowers the cost of production;

muslims control the north africa during the period of 1500 up

to 1800. they made a barrier to prevent further european exploration from

entering the africa from the north. however, the dutch ware still able to move

toward the interior with having south africa as one of the routes leading to

the east for trading with asia.