Question

(a) What is the actual cost incurred in producing the 1051st and the 2191st disc? (Round your answers to the nearest cent.)

Answer 1

This question is incomplete, the complete question is;

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 ≤ x ≤ 6000) .

(a) What is the actual cost incurred in producing the 1051st and the 2191st disc? (Round your answers to the nearest cent.)

(b) What is the marginal cost when x = 1050 and 2190? (Round your answers to the nearest cent.)

Answer:

a)

Actual cost for 1051st disc is $1.79

Actual cost for 2191st disc is $1.56

b)

the marginal cost are;

C'(1050) = $1.79

C'(2190) =  $1.56

Step-by-step explanation:

Given the data in the question;

C(x) = 2000 + 2x -0.0001x²

a)

What is the actual cost incurred in producing the 1051st and the 2191st disc? (Round your answers to the nearest cent.)

Actual cost for 1051st disc will be;

⇒ C(1051) - C(1050)  

= [ 2000 + 2(1051) - 0.0001×(1051)²] - [ 2000 + 2(1050) - 0.0001×(1050)² ]

= [ 2000 + 2102 - 110.4601 ] - [ 2000 + 2100 - 110.25 =

= 3991.5399 - 3989.75

= $ 1.7899 ≈ $1.79

Actual cost for 2191st disc will be;

⇒ C(2191) - C(2190)  

= [ 2000 + 2(2191) - 0.0001×(2191)²] - [ 2000 + 2(2190) - 0.0001×(2190)² ]

= [ 2000 + 4382 - 480.0481 ] - [ 2000 + 4380 - 479.61 ]

= 5901.9519 - 5900.39

= $ 1.5619 ≈ $1.56

Therefore,

Actual cost for 1051st disc is $1.79

Actual cost for 2191st disc is $1.56

b)

What is the marginal cost when x = 1050 and 2190? (Round your answers to the nearest cent.)

Marginal cost is; C'(x) = 2 - 0.0002x

so;

C'(1050) = 2 - 0.0002(1050) = 2 - 0.21 = $1.79

C'(2190) = 2 - 0.0002(2190) = 2 - 0.438 = $1.562 ≈ $1.56

Therefore; the marginal cost is;

C'(1050) = $1.79

C'(2190) =  $1.56