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A developer is planning a fence around a rectangular field. They are using three different types of fencing. The fencing on the north side will cost $50 per metre, the fencing against the south side will cost $70 per metre and the fencing for the other two sides will cost $100 per metre. If the developer only has $7000 to spend, determine using calculus methods the dimensions of the field that will maximise the enclosed area.

A developer is planning a fence around a rectangular field. They are using three different types of fencing. The fencing on the north side will cost $50 per metre, the fencing against the south side will cost $70 per metre and the fencing for the other two sides will cost $100 per metre. If the developer only has $7000 to spend, determine using calculus methods the dimensions of the field that will maximise the enclosed area.

College Algebra (MindTap Course List)
College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter6: Linear Systems
Section6.8: Linear Programming
Problem 5SC: If during the following year it is predicted that each comedy skit will generate 30 thousand and...
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8. A developer is planning a fence around a rectangular field. They are using three different types of fencing. The fencing on the north side will cost $50 per metre, the fencing against the south side will cost $70 per metre and the fencing for the other two sides will cost $100 per metre. If the developer only has $7000 to spend, determine using calculus methods the dimensions of the field that will maximise the enclosed area.
Transcribed Image Text:8. A developer is planning a fence around a rectangular field. They are using three different types of fencing. The fencing on the north side will cost $50 per metre, the fencing against the south side will cost $70 per metre and the fencing for the other two sides will cost $100 per metre. If the developer only has $7000 to spend, determine using calculus methods the dimensions of the field that will maximise the enclosed area.
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