An apple farm yields an average of bushels of apples per tree when trees are planted on an acre of ground. Each time 1 more tree is planted per acre, the yield decreases by 1 bushel (bu) per tree as a result of crowding. How many trees should be planted on an acre in order to get the highest yield?

33 trees

Step-by-step explanation:

Let us assume the number of trees planed for receiving greatest yield is be x

Now the equation would be

f(x) = (21 + x) (45 - x)

= -x^2 + 24x + 945

Now we have to differentiate the f with regard to x

Now as it can be seen that

f is at maximum when x = 12

So, the number of trees would be

= 21 + 12

= 33 trees

answer: expected value of x = 1.0

step-by-step explanation:

p(x=0) = 0.25

p(x=1) = 0.50

p(x=2) = 0.25

expected value for x = 0×0.25 + 1×0.5 + 2×0.25 = 1.0