Rate problem - when should the cow be sold?

[Anabelle37]

Homework Statement

A cow weighing 500kg gains 5kg/day and costs $1 a day to keep. the market price for the cattle is $15 per koliram, but is falling by 10cents per day. when should the cow be sold?

Homework Equations

The Attempt at a Solution

so the 500kg is the initial condition to the problem. To figure out when the cow should be sold I was trying to work out (the rate of which it increases in value) - (the rate it decreases its value) = the rate of change of the price of the cow. Once i find the rate of change of the price of the cow i would set that to zero to find t which corresponds to the time when the market price of the cow is maximum.

I'm having trouble with the expressions for rate in terms of the values/information given.
Any help would be great!

 

[fzero]

You want to determine the value of the cow after t days, as well as the cost of keeping the cow for t days. The difference of these is the profit as a function of t. You want to find the value of t for which the profit is at a maximum.