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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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