What do you think is the most important thing an advertising professional must remember when using social media?

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

3 years ago

Watters Umbrella Corp. issued 15-year binds two years ago at a coupon rate of 6.2 percent. The bonds make semiannual payments. I

Sholpan [36]

Answer:

YTM = 6.42%

Explanation:

current market value = $1,000 x 98% = $980

n = (15 - 2) x 2 = 26

coupon = $1,000 x 6.2% x 1/2 = $31

face value = $1,000

YTM = [coupon + [(face value - market value)/n]} / [(face value + market value)/2]

YTM = [31 + [(1,000 - 980)/26]} / [(1,000 + 980)/2]

YTM = (31 + 0.77) / 990 = 31.77 / 990 = 0.03209 x 2 (annual yield) = 0.641818 = 6.42%

5 0

2 years ago

The price of stadium seats at a baseball game increases from $20 to $30 and ticket sales fall from 45,000 per game to 35,000 per

Xelga [282]

Answer:

Inelastic

Explanation:

Price Elasticity of demand is the a measure which is used to show the responsiveness of the quantity to its price.

Price Elasticity of demand = Change in quantity / Change in price

% Change in quantity = ( 45,000 - 35,000 ) / 45,000 = 22.22%

% Change in price = ( 20 - 30 ) / 20 = -50%

Price Elasticity of demand = Change in quantity / Change in price

Price Elasticity of demand = 22.22% / -50% = -0.4444

As the answer is less than 1 so, demand is Inelastic.

8 0

3 years ago

During the year, Kim sold the following assets: business auto for a $1,000 loss, stock investment for a $1,000 loss, and pleasur

Anton [14]

Answer:

c. $2,000

Explanation:

total loss claim = business auto loss + stock investment loss

= $1,000 + $1,000

= $2,000

Therefore, The Kim may claim $2,000 of these losses.

3 0

3 years ago

Looking again at bank a and bank b, based on the information available, which bank do you think is at the greatest risk of insol

Kazeer [188]

<span>The greatest risk of insolvency</span> can be determined with a variety of factors.

5 0

3 years ago