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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

Suppose a bond with a 10% coupon rate and annual coupons, has a face value of $1,000, 5 years to maturity and is selling for $1,

Taya2010 [7]

<u>Solution and Explanation:</u>

1. the Yield to maturity

FV = 1,000

PMT = FV multiply with Coupon rate , PMT = 1,000 multiply with 0.1 = 100

N = 5 , PV = -1,197.93

CPT I/Y

I/Y = 5.380166647

Therefore, the Yield to maturity = 5.380166647%

Where: FV – fair value, PV – Present value

2. Current yield = Coupon payment divided by Price

Current yield = 100 divided by 1,197.93

By solving we get,

Current yield = 0.08347733173

Therefore, the Current yield = 8.347733173%

7 0

3 years ago

I help back so please help me. also i have uploaded many questions today if you want a lot of points...

7nadin3 [17]

I think the 2nd option is the answer.

6 0

3 years ago

Read 2 more answers

Pauley Company needs to determine a markup for a new product. Pauley expects to sell 22,000 units and wants a target profit of $

Sever21 [200]

Answer:

variable markup % = 60%

Explanation:

total units sold 22,000

total costs associated with selling the 22,000 units:

variable production costs $18 x 22,000 = $396,000

variable S&A costs $13 x 22,000 = $286,000

fixed overhead = $20,500

fixed S&A = $36,700

total costs = $739,200

total cost per unit = $33.60

selling price = $33.60 + $16 = $49.60

markup percentage = [(sales price - unit cost) / unit cost] x 100

the total markup % = [49.60 - 33.60) / 33.60] x 100 = 47.62%

but since we are going to calculate the markup percentage solely based on variable costs, then:

variable cost per unit = $31

selling price = $49.60

the variable markup % = [49.60 - 31) / 31] x 100 = 60%

8 0

3 years ago

Jack and jill have just had their first child. if college is expected to cost $180 comma 000180,000 per year in 1818 years, ho

oksano4ka [1.4K]

Given:
tuition: 180,000 per year
period to save: 18 years
annual rate of return : 6%

FV = PV * (1+r)^t
180,000 = PV * (1 + 0.06)¹⁸
180,000 = PV * (1.06)¹⁸
PV = 180,000 / (1.06)¹⁸ = 180,000 / 2.854 = 63,069.38

Jack and Jill will have to invest 63,069.38 in the first year to have a total of 180,000 after 18 years.

Using Future Value Annuity formula:

FV of Annuity = P [{(1+r)^n - 1} / r]

180,000 = P [{(1.06)¹⁸ - 1} / 0.06]
180,000 = P (30.906)
P = 180,000 / 30.906
P = 5,824.11

Jack and Jill will have to deposit 5,824.11 every end of the year for the total to reach 180,000 after 18 years.

8 0

3 years ago