function Q: When should the steer be sold to maximize profit

[fred2028]

A 135-kg steer (cow) gains 3.5 kg/day and costs 80 cents/day to keep. The market price for beef cattle is $1.65/kg, but the price falls by 1 cent/day. When should the steer be sold to maximize profit?

 

[stapel]

What have you tried? (For instance, what numbers have you plugged in, in an attempt to find a pattern that could be turned into a formula?) How far have you gotten? Where are you stuck?

Thank you.

Eliz.

 

[fred2028]

What have you tried? (For instance, what numbers have you plugged in, in an attempt to find a pattern that could be turned into a formula?) How far have you gotten? Where are you stuck?

I've come up with the following equation, but I doubt it's right ...

P(t)=1.65(135+3.5t)-0.8t-0.01(135+3.5t)

 

[tkhunny]

You are SO close. I didn't expect the correct formulation to be linear. This causes me to wonder about that last term.

You should have 0.01*t*(Steer Mass). That extra 't' will do it.

Note: you will have to make a choice in here, somewhere. Is this an INTEGER problem? If it is, you can't solve it like any old parabola problem. You'll have to find the continuous solution and hope the integer solution is hanging around there.