QUADRATIC FUNCTIONS HELP, please please please!?

Question

A Super Lemon currently weighs 100 kg and is increasing by 4 kg per day. The price for Super Lemons is currently 8.90 per kilogram but is decreasing at $0.30 per kg per day. The cost to grow the lemon is $0.80 per day. Determine how many days from now the lemon should be sold to maximize profit and what the maximum profit will be.

Help me solve this please? I am so lost.

Answer 1

Set up the profit equation:
P = (100 + 4t)(8.9 - 0.3t) - 0.8t
P = 890 - 30t + 35.6t - 1.2t^2 - 0.8t
P = 890 + 4.8t - 1.2t^2
Take the derivative and set it equal to zero:
dP/dt = 4.8 - 2.4t = 0
2.4t = 4.8
t = 2 days
P = (100 + 4(2))(8.9 - 0.3(2)) - 0.8(2)
P = (108)(8.3) - 1.6
P = $894.80