The number N of cars produced at a certain factory in 1 day after t hours....

[Bre-An]

The number N of cars produced at a certain factory in 1 day after t hours of operation is given by N(t)=700t-10t^2, 0(less than or equal to) t (less than or equal to) 10. If the cost C (in dollars) of producing N cars is C(N)=30,000+5000N, find the cost of C as a function of the time of operation of the factory.

 

[Deleted member 4993]

The number N of cars produced at a certain factory in 1 day after t hours of operation is given by

N(t)=700t-10t^2, 0 <= t <= 10. .....................................(1)

If the cost C (in dollars) of producing N cars is

C(N)=30,000+5000N .....................................................(2)

find the cost of C as a function of the time of operation of the factory.

Replace N in the equation (2) by right-hand-side of the equation (1).

What do you get?

 

[ksdhart]

Alright, well, the cost C is a function of N. But N is itself a function of t. So what if you rewrote the cost function? Then you'd have: C(N(t)) = 30000 + 5000 * N(t). Does that help?

 

[Bre-An]

Oh!
I would get 700(30000+5000N)-10(30000+5000N)^2

 

[Bre-An]

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:smile:

 

[ksdhart]

That's not quite right, either. The expression you posted was created by taking the formula for N and plugging in C(N) as a parameter. Can you see why evaluating N(C(N)) doesn't make any sense? Remember your task - express the cost in terms of time.

 

[Deleted member 4993]

The number N of cars produced at a certain factory in 1 day after t hours of operation is given by N(t)=700t-10t^2, 0(less than or equal to) t (less than or equal to) 10. If the cost C (in dollars) of producing N cars is C(N)=30,000+5000N, find the cost of C as a function of the time of operation of the factory.

It should be:

C(N)=30,000+5000N

C(t)=30,000+5000(700t-10t^2) = -50000*t^2 + 3500000*t + 30000

Now you have C as a function of 't'.