Science:Math Exam Resources/Courses/MATH110/April 2014/Question 04
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Question 04 

A farmer wants to enclose a rectangular pasture of square metres. Three sides of the pasture will be enclosed with cedar fencing at a cost of $ per metre. The remaining side is to be enclosed with a stone wall at a cost of $ per metre. What should the dimensions of the field be to minimize the cost of the enclosure? 
Make sure you understand the problem fully: What is the question asking you to do? Are there specific conditions or constraints that you should take note of? How will you know if your answer is correct from your work only? Can you rephrase the question in your own words in a way that makes sense to you? 
If you are stuck, check the hints below. Read the first one and consider it for a while. Does it give you a new idea on how to approach the problem? If so, try it! If after a while you are still stuck, go for the next hint. 
Hint 1 

Draw a diagram to illustrate the setting and label the diagram with variables that might be useful later. 
Hint 2 

What is the variable that we are trying to optimise? 
Hint 3 

What equations might be useful in relating the variables we have? 
Hint 4 

Can we express the variable we are trying to optimise as a function of a single variable? 
Checking a solution serves two purposes: helping you if, after having used all the hints, you still are stuck on the problem; or if you have solved the problem and would like to check your work.

Solution  

Found a typo? Is this solution unclear? Let us know here.
Please rate my easiness! It's quick and helps everyone guide their studies. We proceed using the standard template for solving optimisation questions. The exact steps might vary between course and section, but the overall steps will be similar.
