Question

The total cost (in dollars) of producing x food processors is C(x) = 2500 + 50x -0.28.

Answer 1

Answer:

The exact cost of producing the 21st food processor is $38.52.

The marginal cost to approximate the cost of producing the 21st food processor is $38.24

Step-by-step explanation:

Consider the provided function.

$C(x) = 2500 + 50x -0.28x^2$

(A) Find the exact cost of producing the 21st food processor

The exact cost producing 21st food processor is C(21)-C(20)

Substitute x=21 in above function.

$C(x) = 2500 + 50(21) -0.28(21)^2$

$C(x) = 2500 +1050 -123.48$

$C(x) = 3426.52$

Substitute x=20 in above function.

$C(x) = 2500 + 50(20) -0.28(20)^2$

$C(x) = 2500 +1000-112$

$C(x) = 3388$

The exact cost producing is:

$C(21)-C(20)=3426.52-3388=38.52$

Hence, the exact cost of producing the 21st food processor is $38.52.

Part (B) Use the marginal cost to approximate the cost of producing the 21st food processor,

To find the marginal cost first differentiate the function with respect to x.

$C(x) = 2500 + 50x -0.28x^2$

$C'(x) =50-0.56x$

Now substitute x=21 in above function.

$C'(x) =50-0.56(21)$

$C'(x) =50-11.76$

$C'(x) =38.24$

The marginal cost to approximate the cost of producing the 21st food processor is $38.24