Max Profit Calc: Sell Farmer's Crop by Oct 10

[Grif1]

Homework Statement

A farmer can sell his crop for p= -t^2+60t+100 dollars per ton, where p is price and t is the number of days after Oct. 1st. Additionally, the farmer must sell his crop on or before Oct. 10 to pay his outstanding credit card bills. On what day should he sell to maximize profit?

Homework Equations

The Attempt at a Solution

 

[daveb]

What have you attempted so far, and where are you stuck?

 

[Grif1]

I get -2t + 60 = 0
-2t = -60
t=30
Multiple choice answers give 8 options from Oct. 4th through Oct. 11?

 

[berkeman]

Homework Statement

A farmer can sell his crop for p= -t^2+60t+100 dollars per ton, where p is price and t is the number of days after Oct. 1st. Additionally, the farmer must sell his crop on or before Oct. 10 to pay his outstanding credit card bills. On what day should he sell to maximize profit?

Homework Equations

The Attempt at a Solution

I get -2t + 60 = 0
-2t = -60
t=30
Multiple choice answers give 8 options from Oct. 4th through Oct. 11?

How does the additional constraint stated in the problem change your answer?

 

[SteamKing]

Selling price is not necessarily equal to profit. Have you provided all parts of the problem you were asked to solve?

 

[Grif1]

I'm confident t=30 is correct, but is the day to sell to max profit Oct. 31? As t = # of days after Oct. 1. Oct. 31 is not one of the multiple choice options?

 

[Grif1]

Yes.

 

[daveb]

When looking for a max (or min) of a function, you also look at the endpoints of the interval over which the function is defined, in this case, at t = 0 and t = 9 (not t = 10 since Oct 1 is day 0)