Math Modeling : One-Variable Optimization
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Example Question #1 : 5 Step Method
A cow that weighs 175 pounds gains 3 pounds per day, and it costs 30 cents per day to keep that cow. The market price for cows is 75 cents per pound, but the price is falling one cent per day. When should the cow be sold to make the maximum profit?
Use the 5-step method.
The cow should be sold after 4 days.
The max profit is $151.58.
The cow should be sold after 2 days.
The max profit is $131.58.
The cow should be sold after 3 days.
The cow should be sold after 3 days.
The 5-step method for this particular modeling question is as follows.
1. Ask the question
When should the cow be sold to make the maximum profit?
Now identify all known information.
Variables:
2. Select the modeling approach
For this particular question the function can be define 
3. Formulate the model
To maximize 
Now rewrite the equation in terms of 
4. Solve the model
Now to solve the model, take the derivative, set it equal to zero, and solve for 
5. Answer the question
The cow should be sold after 3 days.
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