Gr 12 Calc: Optimization problem/min cost

[Specter]

Homework Statement

A homeowner wishes to enclose a rectangular garden with fencing. The garden will be adjacent to his neighbour’s lot. There will be fencing on all four sides. His neighbour will be paying for half the shared fence

1. What should the dimensions of the garden be if the area is 432 m^2 and the homeowner would like to keep his share of the cost to a minimum? Include a diagram.
2. At $45/m, what is the homeowner’s cost? What is the neighbour’s cost?

Homework Equations

The Attempt at a Solution

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My diagram https://i.imgur.com/4Pvpxg3.jpg

From there I know that I need to find what y equals but this is where I get stuck. After I find y I need to find
the side of the fence that is shared with the neighbour. Then I can set up a cost function. I haven't done any questions like this before so I am struggling. I guess I just need some help setting up the problem. Thanks

 

[BvU]

Then I can set up a cost function

Make an attempt... you know the price per meter, you want to know the cost, so you'll need ...

Oh, and read the guidelines, about this required attempt and about posting pictures directly, not on some temporary cookiemonster