A 60,000 square meter rectangular yard is to be enclosed on three sides by wood fencing that costs $25.00 per meter and on the fourth side with a stone wall that will cost $40.00 per meter. What is the minimum cost of enclosing this yard as described?

And we can solve for y and we got:

And using condition (1) we can solve for x and we got:

So then the minimum cost for this case would be:

Explanation:

For this case the graph attached illustrate the problem for this case

We know that the total area is 60000, so then we have:

If we solve for x we got:

 (1)

Now we can define the cost function like this:

We can use the condition (1) and if we replace in the cost function we have:

Since we need to minimize the cost, we can derivate the function in terms of y and we got:

And we can solve for y and we got:

And using condition (1) we can solve for x and we got:

So then the minimum cost for this case would be:

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