Hm...not too sure about this one?

Question

The yield of a crop, in tonnes, is dependant upon the time, t, in days, between planting and harvesting, according to the follwoing formula.
Y(t) = {80t - t^2 - 1500 if t is an element of [30,50]
0 if t is an element of [0, 30)
or t is an element of (5, infinity)

On which day is the maximum yield reached, and what is the maximum yield?

Answer 1

So, for the time t = 30 to 50,
Y(t) = 80t - t² - 1500

Y'(t) = 80 - 2t
0 = 80 - 2t
2t = 80
t = 40

Since the parabola opens downward, this must be a local maximum.

The maximum yield is reached when t = 40.
The maximum yield is 100 tonnes.

Answer 2

You can eliminate 0-30 days because at some point you will have some yield. Also, I think you mean "t if it is an element of (50,infinity)."

Take the derivative of y=80t-t^2-1500
dy/dx=80-2t Set equal to 0 and solve for t
0=80-2t
2t=80
t=40 Plug into formula
80(40)-(40)^2-1500
3200-1600-1500=100
Your maximum yield between 30-50 days is 100 tonnes after 40 days. However, since the yield in tonnes is equal to the number of days if it is after the 50th day, then any day from [101, infinity) would produce more than 100 tonnes. Since it can apparently go on for an infinite amount of time, then you can't find a maximum, because you can never reach infinity.

Answer 3

max is at t = 80 ( by differentiating Y(t) -> Y' solve Y'=0

Answer 4

Could you rephrase your question more clearly?

There seems to be some confusion...