Answer:
A) t = 2.6 weeks
B) R = $329.48
Step-by-step explanation:
At the right time, the average amount of money made from the fruits is given as
R = (selling price of fruits per pound) × (average number of pounds of fruits) = 2.4 × 137 = $328.8 on average.
So, delaying the harvest by a week makes the revenue turn to
R = (2.4 - 0.04)(137 + 2.5)
Delaying the harvest by t weeks makes the revenue turn to
R = (2.4 - 0.04t) × (137 + 2.5t)
R = 328.8 + 6t - 5.48t - 0.1t²
R(t) = -0.1t² + 0.52t + 328.8
A) Time in weeks when the Revenue would be highest.
That is, value of t that corresponds to the maximum value of R(t)
At maximum value, (dR/dt) = 0 and (d²R/dt²) < 0, that is negative.
R(t) = -0.1t² + 0.52t + 328.8
(dR/dt) = -0.2t + 0.52 = 0
and (d²R/dt²) = -0.2 < 0 (negative; this is indeed a maximum point for the function)
When (dR/dt) = 0,
(dR/dt) = -0.2t + 0.52 = 0
-0.2t + 0.52 = 0
t = (0.52/0.2)
t = 2.6 weeks.
B) Actual Maximum value of the Revenue.
This corresponds to the revenue when t = 2.6 weeks
R(t) = -0.1t² + 0.52t + 328.8
R(2.6) = -0.1(2.6)² + 0.52(2.6) + 328.8
R(t = 2.6) = -0.676 + 1.352 + 328.8
R at maximum point = $329.48
Hope this Helps!!!
