struggle with marginal cost's

[Sophie]

Hello

I am 90% sure the calculuc is right on the following question, but I am not sure I have worded the answer right.

Suppose that C(x) = (0.001x^3) - (0.6x^2) + 92x +750

a. Find the production level that minimizes the marginal cost.

C'(x) = (0.003x^2) - 1.2x + 92
C''(x) = 0.006x - 1.2
C''(x) = 0 when x = 200

C'''(x) = 0.006 which is greater than 0, therefore x is a minimum

OK here is where I get stuck... how I interprit the above information... I understand the above to mean the following 2 things, but only 1 can be right or neither maybe! If someone could clarify the below I would be very greatful...

When the 201st unit is produced the marginal cost is at a minimum.
or
When the production level reaches 200 units the marginal costs are at a minimum.

Thanks for your time, Sophie

 

[morson]

No, your calculus is not right. It is entirely wrong. Judging by the other thread and this, you might want to review differentiation.

 

[sky2rain]

The differentiation is absolutely flawless. The model C(x) is determining the Total Cost, and first differentiation determines the Marginal Cost of the production. Second differentiation is going to tell us the change in Marginal Cost. When producing the 200th unit, marginal cost is -28 (the number can be negative, think if you bulk purchase the raw material for production, your total cost can be lower than before), which is the lowest point on the graph. (If you do a graph, you will need to do the first differentiation because the original equation won't give you anything but total production cost.

 

[sky2rain]

having done the graph, you will see the 199th unit's marginal cost is -27.997 and 201th unit's marginal cost is -27.997, they are both higher than -28.

 

[skeeter]

The differentiation is absolutely flawless.

izzatso? take another L:shock::shock:K ...

Suppose that C(x) = (0.001x^3) - (0.6x^2) + 92x +750

a. Find the production level that minimizes the marginal cost.

C'(x) = (0.006x^2) - 1.2x + 92

 

[sky2rain]

I think that's a typo, not really a mistake. If she continued to derive the second derivitive based on that error, she should get 0.012x - 1.2 as a result

I'd reconsider what I have said about bulk-purchases on raw materials, it's not a good example here because bulk purchases' total price is always increasing. A good example should be government subsidized production, if you really try to see some sense out of the total cost equation.

 

[Sophie]

Thanks for everyones input.

I have edited my answer, it was a typo.

Now going by sky2rain's information I think the following interpretation of the the production level is correct:

When the 201st unit is produced the marginal cost is at a minimum.

Thanks Sophie

 

[sky2rain]

Maybe I didn't explain it clearly. Let's put it in plain real world languange, when producing the 199th unit after the 198th, the factory saved 27.997 on producing this one extra unit. When producing the 200th after the 199th, the factory saved 28 on producing this one extra unit, when producing the 201st after the 200th, the factory saved 27.997 on this one extra unit. Now you tell me on producing which unit the factory saved the most?