Sally promotes her sunscreen product by claiming that with just one

An oil refinery is located on the north bank of a straight river that is 3km wide. A pipeline is to be constructed from the refi

Mariulka [41]

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:

$\sqrt{3^{2} +x^{2}}=\\\sqrt{9 +x^{2}}$

And we multiply it by 1,000,000; the cost of laying pipe under the river, the we get:

$1000000\sqrt{9+x^{2}$

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:

$f(x)=1000000\sqrt{9+x^{2}} + 500000(8-x)$

<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>

$f(x)=1000000\sqrt{9+x^{2}} + 500000(8-x)\\f(x)=1000000(9+x^{2})^{1/2}+4000000-500000x\\f'(x)=\frac{1}{2} 1000000(9+x^{2})^{-1/2}(2x)-500000\\\\f'(x)=\frac{1000000x}{\sqrt{9+x^2}} - 500000$

$f'(x)=\frac{1000000x}{\sqrt{9+x^2}} - 500000=0\\\frac{1000000x}{\sqrt{9+x^2}} = 500000\\\frac{2x}{\sqrt{9+x^2}} = 1\\2x={\sqrt{9+x^2}}\\4x^2=9+x^2\\3x^2=9\\x^2=3\\x=\sqrt{3} \\$

And we plug square root of 3 in the original cost function ad we get

$f(\sqrt{3} )=1000000\sqrt{9+x^{2}} + 500000(8-x)\\f(\sqrt{3})=1000000\sqrt{9+(\sqrt{3} )^{2}} + 500000(8-(\sqrt{3}))\\f(\sqrt{3})=1000000\sqrt{9+3} + 500000(8-(\sqrt{3}))\\f(\sqrt{3})=1000000\sqrt{12}+500000(6.27)\\f(\sqrt{3})=1000000(3.46)+500000(6.27)\\f(\sqrt{3})=3464101.62+3133974.60\\f(\sqrt{3})=6598076.21\\$

<h2>so the minimal cost is $6,598,076.21</h2><h2 /><h3 />

6 0

4 years ago

True or false: the process of taking notes about security and security routines is an example of an adversarial surveillance act

HACTEHA [7]

True because they take notes on the security and the routines.

5 0

4 years ago

In 2017, Orear Manufacturing signed a contract with a supplier to purchase raw materials in 2018 for $700,000. Before the Decemb

MArishka [77]

Answer:

d) as a current liability

Explanation:

Current Liabilities are those liabilities which are payable within one years time e.g trade payable, tax payable etc.

The credit against the purchase of inventory is classified as the trade payable and it is paid in a short time, so it will be reported on the balance sheet in current liability section.

5 0

3 years ago

Suppose your manager wanted you to copy two other managers on the survey email to your coworker. Where would you put the manager

liberstina [14]

Answer: Idk :\ good luck tho

3 0

3 years ago

Which of the following is not an input to the aggregate planning process? A. demand forecast B. cost information C. policies on

ale4655 [162]

Answer:

The correct answer is E. master production schedules.

Explanation:

Master production schedules is not an input to the aggregate planning process all other options are its input,

Aggregate planning process is an attempt to respond to predicted demand within the constraints set by product, process and location decisions.

Hence, master production schedules is not a relevant input for this planning process but can be a result of the aggregate planning process. In other words master production schedule is formed after aggregated planning has been completed.

6 0

3 years ago

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