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
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