9.7: The total cost​ (in dollars) of producing x food processors is ​C(x)=2200+60x−0.4x^2.

Question

The total cost​ (in dollars) of producing x food processors is ​C(x)=2200+60x−0.4x^2.

​(A) Find the exact cost of producing the 51st food processor.

​(B) Use the marginal cost to approximate the cost of producing the 51st food processor.

Answer 1

To start, we have to understand what marginal cost is. Marginal cost is the cost of producing AN ADDITIONAL unit. So if we simply want to know the total cost of producing x food processors, we would set x equal to 51 and solve the problem algebraically. That will give you the total cost - plug plug 51 in for x. Think of marginal as an extra unit..and since we already know x I equal to 51, you will want to subtract that same formula setting x equal to 50 - 51-50=1 unit difference.

Using the total cost function, you could find the cost of producing an additional unit at any level of production.

Answer 2

[2200 +60(51)-(0.4)(51)²] - [2200 + 60(50)-(0.4)(50)²]

[3060 - 0.4*2601] - [3000 - 0.4*2500]

[3060 - 1040.4] - [3000 - 1000]

[2019.6 - 2000]

19.6

C' = 60 - 0.8x

C' = 60 - 40

C' = 20