Question

Recall that to find the cost to produce the nth unit in a production process, we calculate the difference

C(n) – C(n-1)
where C(n) is the cost of producing n units.
The total cost (in dollars) for a fast food franchise of producing x thousand hamburgers might be C(x) = 23000 + 1000x - 70x^2. Find the exact cost of producing the 2,001st burger. Be careful though. The units for x are thousand of hamburgers. The 2,001st burger is represented by 2.001!
Exact cost of 2,001st burger = exist ______ Use marginal cost to approximate the cost of producing the 2001st burger. Approx. cost of 2001st burger = exist ______

Answer 1

The exact cost of producing the 2,001st burger is $25,720.86. The approximate cost of producing the 2001st burger using marginal cost is $21,720.

Step-by-step explanation:

To find the exact cost of producing the 2,001st burger, we need to calculate the difference between C(2.001) and C(2). Plugging the values into the equation C(x) = 23000 + 1000x - 70x², we have:

C(2.001) = 23000 + 1000(2.001) - 70(2.001)²
= 23000 + 2001 - 280.14
= 25,720.86

The exact cost of producing the 2,001st burger is $25,720.86.

To approximate the cost of producing the 2001st burger using marginal cost, we need to find the marginal cost of producing the 2nd burger. Plugging the values into the equation C(x) = 23000 + 1000x - 70x², we have:
C(2) = 23000 + 1000(2) - 70(2)²
= 23000 + 2000 - 280
= 21,720

The approximate cost of producing the 2001st burger using marginal cost is $21,720.