Question

I'd like to know the process to get to the answer please (included)

The total weekly cost (in dollars) incurred by Lincoln Records in pressing x compact discs is given by the following function.
C(x) = 2000 + 2x - 0.0001x2 (0 < (or = to) x < (or = to) 6000)

(a) What is the actual cost incurred in producing the 971st and the 1971st disc? (Round to the nearest cent.)
971st disc $1.81
1971st disc $1.61

(b) What is the marginal cost when x = 970 and 1970? (Round to the nearest cent.)

970 $1.81
1970 $1.61

Answer 1

don't you plug in the number?

Answer 2

\[C(x) = 2000 + 2x - 0.0001x^2\]\[C(971)=2000+2(971)-.0001(971)^2\]?

Answer 3

Did you try it on your calculator?? I tried it and I'm way off so I might be putting it in wrong if you got it like that

Answer 4

part a looks like you're just substituting like satellite73 is showing

part b will involve the derivative of C(x)

Answer 5

or just the slope

Answer 6

oh yeah i am way way off

Answer 7

perhaps it is
\[C(971)-C(970)\] for the actual cost of that disc
lets try it

Answer 8

yay!
http://www.wolframalpha.com/input/?i=2000%2B2%28971%29-.0001%28971%29^2-%282000%2B2%28970%29-.0001%28970%29^2%29

Answer 9

C is the total cost
up until that disc
so the cost of producing that disc is the to total cost up to that one minus the total cost up until the one beofore

Answer 10

Ohhhh ok yay! haha

Answer 11

i believe this is also the marginal cost, unless you are using calculus

Answer 12

Well the answers are the same for A and B so I'm guessing so, thanks!

Answer 13

k they might be the same in any case due to rounding

Answer 14

\[C(x) = 2000 + 2x - 0.0001x^2 \]
\[C'(x) =2 - 0.0002x \]

Answer 15

\[C'(970)=2-.0002\times 970=1.81\] rounded to the nearest penny