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Sladkaya [172]
3 years ago
14

A supply company manufactures copy machines. The unit cost C (the cost in dollars to make each copy machine) depends on the numb

er of machines made. If x machines are made, then the unit cost is given by the function
C (x) = 0.8x ^ 2 - 256x +25,939 . How many machines must be made to minimize the unit cost? Do not round your answer.
Number of copy machines:
Mathematics
2 answers:
Ugo [173]3 years ago
7 0

Answer:

Number of copy machines must be made to minimize the unit cost=160.

Step-by-step explanation:

We are given that the unit cost function C ( the cost in dollars to make each copy machine)

If machines are made =x

Then the unit cost function is given by

C(x)=0.8x^2-256x+25939

We have to find the number of copy machines for  minimize the unit  cost

C(x)=0.8x^2-256x+25939

Differentiate with respect to x

Then we get

\frac{\mathrm{d}C}{\mathrm{d}x}=1.6x-256 ......(equation I)

To find the value of x then we susbtitute \frac{\mathrm{d}C}{\mathrm{d}x} is equal to zero

\frac{\mathrm{d}C}{\mathrm{d}x}=0

1.6x-256=0

1.6x=256

x=\frac{256}{1.6}

By using division property of equality

x= 160

Again differentiate the equation I with respect to x then we get

\frac{\mathrm{d}^2 C}{\mathrm{d}^2 x}=1.6 >0

Hence, the unit cost is minimize for x=160

Therefore, the number of copy machines must be made to minimize the unit cost =160

Ugo [173]3 years ago
4 0
To answer this item, we take the differential of the equation and equate to zero.
 
                  C(x) = 0.8x² - 256x + 25939

Differentiation,
                dC(x) = 1.6x - 256 
                 dC(x) = 1.6x - 256 = 0

The value of x from the derived equation above is 160. 

Thus, the number of machine to be made in order to minimize the cost should be 160. 
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Hello!

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3 years ago
It is a solid shape that contains lateral surface and two circular bases which are parallel and congruent.
ad-work [718]

Answer:

B (cylinder)

Step-by-step explanation:

Two <u>circular</u> bases which are parallel and congruent :

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The cube doesn't have any circular bases.

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A cone has a circular base, but it doesn't have two.

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8 0
2 years ago
The diagram represents the shape and dimensions of Kayla's garden. A special fertilizer is used for the vegetable garden. Each b
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Answer:

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Step-by-step explanation:

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A = L\times W

So let's solve it:

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With that, we can figure out how many bags of fertilizer would be needed by dividing the area of the vegetable garden by how much one bag of fertilizer covers:

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3 0
2 years ago
Read 2 more answers
Multiply each equation by a constant that would help to eliminate the y terms.
Zinaida [17]

Answer:

Therefore the required resulting equation is

6x-15y=-63\\-15x+15y=90

6 x minus 15 y = negative 63.

Negative 15 x + 15 y = 90

Step-by-step explanation:

Given:

2x-5y=-21         ......................Equation ( 1 )

3x-3y=-18         ......................Equation ( 2 )

To Find:

Expression after multiplying to eliminate y term,

Solution:

So to eliminate 'y' term we need to multiply equation 1 by a constant 3 and equation 2 by a constant -5,  such that equations  becomes

3(2x-5y)=3\times -21\\\\6x-15y=-63 .....( 1 )

-5(3x-3y)=-5\times -18\\\\-15x+15y=90  .....( 2 )

so now by adding new equation one and two we can eliminate y term that means -15y and +15y will get cancel,

Therefore the required resulting equation is

6x-15y=-63\\-15x+15y=90

6 x minus 15 y = negative 63.

Negative 15 x + 15 y = 90

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2 years ago
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