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 (0x 6000)

(a) What is the actual cost incurred in producing the 1041st and the 2141st disc? (Round your answers to the nearest cent.)


1041st disc

$ ??

2141st disc

$ ??

(b) What is the marginal cost when x = 1040 and 2140? (Round your answers to the nearest cent.)

1040

$ ??

2140

$ ??

To find the actual cost incurred in producing the 1041st and 2141st disc, we need to substitute the respective values of x into the function C(x) = 2000 + 2x - 0.0001x^2.

(a)
1. For the 1041st disc:
Substitute x = 1041 into the function:
C(1041) = 2000 + 2(1041) - 0.0001(1041)^2
Calculate the value to find the actual cost.

2. For the 2141st disc:
Substitute x = 2141 into the function:
C(2141) = 2000 + 2(2141) - 0.0001(2141)^2
Calculate the value to find the actual cost.

(b)
To find the marginal cost when x = 1040 and 2140, we need to calculate the derivative of the function C(x) with respect to x. The derivative will give us the rate of change of the cost with respect to the number of discs being produced at a given point.

2. Calculate the derivative of C(x) to get the marginal cost function.

3. Evaluate the marginal cost function at x = 1040 to find the marginal cost for the 1040th disc.

4. Evaluate the marginal cost function at x = 2140 to find the marginal cost for the 2140th disc.

Once you have followed these steps, you will get the answers to the questions.