Answer:
To properly answer this question, let us first define what marginal cost is:
Marginal cost can be defined or refers to the rate of change of the total cost.
Referencing back to the question on how to get the fixed cost , we can do this by integrating the marginal cost function. Also, the fixed cost is given in the question which is the total cost when the production is zero. By using this, we can find the value of integration constant which will appear in the total cost function
Therefore,
∫ xⁿdx ****= xⁿ⁺¹/n+1
M
C = 10 - x / 10000
dc/dx = 10 - x / 10000
At this point, we try to separate the variables:
dc = [ 10 - x / 10000 ] dx
After the separation, we perform the integration on both sides:
∫ dc = ∫ [ 10 - x / 10000 ] dx
Recalling that K here is the constant of integration, we then have:
c = 10x - x² / 15000 + k
Also, referencing back to the question, we note that fixed cost is the total cost when the production level is zero, that is C = 15000
, when x = 0
.
Therefore:
15000 = 10 (0) - (0)² / 15000 + k
15000 = 0 + k
k = 15000
c = 10x - x² / 15000 + k
c = 10x - x² / 15000 + 15000
Therefore, the total cost function is:
C = 10 x - x² / 15000 + 15000
So, in summary, the cost of function can be said to be C = 10 x - x² / 15000 + 15000
