Rate problem - when should the cow be sold?

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In summary, the problem involves a cow weighing 500kg that gains 5kg per day and costs $1 per day to keep. The market price for the cow is $15 per kilogram, but decreases by 10 cents per day. The goal is to determine when the cow should be sold to maximize profit, using the initial weight and rate of increase, cost of keeping, and market price decrease rate.
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Anabelle37
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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!
 
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  • #2
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.
 

1. When should the cow be sold?

The ideal time to sell a cow depends on several factors, such as the cow's health, age, and market conditions. Generally, cows should be sold when they have reached their optimal weight and condition for the market. This is usually between the ages of 1-2 years for beef cows and 3-4 years for dairy cows.

2. How do you determine the optimal weight for selling a cow?

The optimal weight for selling a cow is determined by the breed, gender, and intended use of the cow. It is important to consult with a veterinarian or livestock specialist to determine the ideal weight for your specific cow. Factors such as body condition score and frame size also play a role in determining the optimal weight for selling a cow.

3. What are the market conditions that should be considered when selling a cow?

Market conditions refer to the current demand and prices for cows in the market. It is important to research and monitor the market before deciding to sell a cow. Factors such as seasonality, consumer demand, and economic conditions can greatly impact the price of cows. It is also important to consider the cost of transportation and processing fees when selling a cow.

4. Is it more profitable to sell a cow at a specific time of year?

The profitability of selling a cow depends on several factors, such as market conditions, supply and demand, and the cow's age and weight. In general, cows tend to sell for higher prices during peak demand seasons, such as the holiday season or during grilling season. However, it is important to consider all factors and determine the best time to sell based on the individual cow and market conditions.

5. What are the risks of waiting too long to sell a cow?

Waiting too long to sell a cow can result in decreased profitability or even financial losses. As cows age, they may develop health issues or lose weight, decreasing their value in the market. Additionally, market conditions can change quickly, and waiting too long to sell can result in selling during a period of low demand or low prices. It is important to regularly assess the condition and marketability of a cow and make timely decisions on when to sell.

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