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inessss [21]
3 years ago
14

PLEASE HELP!!

Mathematics
1 answer:
geniusboy [140]3 years ago
6 0
I think the answer is about 3905 minutes. Hope this helps!
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A vehide factory manufactures cars. The unit cost C (the cost in dollars to make each car) depends on the number of cars made. I
Oksi-84 [34.3K]

The cost function is given as,

C(x)=1.1x^2-638x+103259

Obtain the first derivative as,

C^{\prime}(x)=1.1(2x)-638(1)=2.2x-638

Obtain the critical points by equating the first derivative to zero,

C^{\prime}(x)=0\Rightarrow2.2x-638=0\Rightarrow2.2x=638\Rightarrow x=290

Thus, the Cost function has an extrema at point 290.

Apply the second derivative test,

C^{\doubleprime}(x)=\frac{d \square}{dx}(2.2x-638)=2.2

Since the second derivative is positive, the function attains minimum value at the critical point.

Therefore, it is concluded that the cost is minimum at 290.

Substitute the value in the function to obtain the minimum cost,

C_{\min }=C(290)=1.1(290)^2-638(290)+103259=10749

Thus, the minimum unit cost is $10749 which corresponds to 290 units of cars.

3 0
1 year ago
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