could you please correct these two problems?

marginal cost for a determined product is MC=3x+50 and the production of 20 units results in a total cost of $2,000, what is the total cost function?

Integrate MC to get
3/2² + 50x + c

Substitute to find c:
2(400) + 2(20) + c = 2,000

800+40 = 2,000
c= 1,160
3/2² + 50x + 1,160

2- If consumption is $5.8 billion when disposable income is 0, and if the marginal propensity to consume is dc/dy = 1/√(y+9) +0.8


(in billions of dollars) find the national consumption function.


If "y" is disposable income [not national] then:
C = ƒ(y)
MPC = ∂C/∂y
C = ∫ [∂C/∂y] ∂y = ∫ [0.8+1/√(y+9)] ∂y = X + 0.8•y + 2•√(9+y)
C [billions] = X + 0.8•y + 2•√(9+y)

C[y=0] =5.8 billion
5.8 = X + 0.8•0 + 2•√(9+0)
5.8 = X+6
X = 5.8-6 = -0.2

C [billions] = 0.8•y + 2•√(9+y) - 0.2

thank you.

Quote:

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Originally Posted by jhonwashington

marginal cost for a determined product is MC=3x+50 and the production of 20 units results in a total cost of $2,000, what is the total cost function?

Integrate MC to get
1) 3/2² + 50x + c

Substitute to find c:
2) 2(400) + 2(20) + c = 2,000
800+40 = 2,000
c= 1,160

3) 3/2² + 50x + 1,160

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I numbered your equations for convenience.

1) Where did the 'x' go?
1) Should this be an equation or function defintion? It's just an expression.

2) Where did the '3' go?
2) Why is the '2' in the numerator?
2) You did square '20', but there is nothing in your equation #1 to indicate that you should have done that.
2) The equation did come back!

3) Where did the 'x' go?
3) Where did the equation go again?

Use very careful and consistent notation.