Answer:
$6,598,076.21
Explanation:
<h2>
THE KEY IS TO FIND OUT THE COST FUNCTION, the calculations are very easy!!!</h2><h2>
</h2><h3>In order to find the cost function, take a look at the drawing attached. </h3>
We can see the river (sort of) that is 3 km wide and the storage tanks on the other side of the river 8 km apart.
<h3 />
Laying pipes under (across) the river costs 1,000,000 the km & laying pipes over land costs 500,000 per km.
<h3 /><h3>So basically the cost function is 1,000,000 multiplied by something plus 500,000 multiplied by another something.</h3><h3 />
The distance across the river can be found by using Pythagoras Theorem. A side is 3 km the other is unknown, so we call it X. And it is equal to:
And we multiply it by 1,000,000; the cost of laying pipe under the river, the we get:
The distance over the land is (8-x), as we can see in the drawing. So we multiply it by its cost, 500,000. And we get 500,000(8-x).
So the cost function f(x) would be:
<h2>From here, we just have to differentiate and the derivative found must be equal to zero in order to minimize cost. </h2><h3>The value of x when the derivative is zero is plugged in the original function to get the cost.</h3><h3 /><h2>LET'S DO THIS</h2>
<h2>f'(x)=0</h2>
And we plug square root of 3 in the original cost function ad we get
<h2>so the minimal cost is $6,598,076.21</h2><h2 /><h3 />
