Difficult word problem below.?

Question

Lucy manages a peach orchard on the western slope. Years of experience have shown that if she plants 80 trees per acre, her yield is 100 pounds of salable peaches per tree. However, for each additional tree per acre that she plants, her yield per tree drops by one pound. How many trees per acre will maximize her yield per acre?

possible solutions, which is correct?
80

85

90

95

Answer 1

Lucy harvests 100 pounds per tree, which means 8,000 pounds per acre, initially.

Let her plant x more trees to get the maximum yield.

The yield per tree becomes 100 - x.

The total number of trees is 80 + x.

The yield is (100 - x)(80 + x) pounds per acre.

This is maximum when the derivative is zero, i.e.

d/dx (8,000 + 20x - x^2) = 0.

i.e. 20 - 2x = 0.

which gives x = 10.

Thus, Lucy should plant 90 trees per acre to maximize her yield.

Answer 2

trees/acre, lbs/Tree, Tot. Lbs
80, 100, 8000
85, 95, 8075
90, 90, 8100
95, 85, 8075

a) 90 per acre

Answer 3

90?

90x90 8100