Respuesta :
Answer:
a) Average price per unit = 700
b) average marginal cost = -1.5 dollars/frame
c) For 201 frames are produced = $698.5
Explanation:
Given Data:
C(x) = 60000 + 400x
a) Average cost for 200 units:
Total Cost of 200 units will be:
C(200) = 60000 + 400(200)
C(200) = 140,000
Total Cost of 200 units = 140,000
Average price per unit = Total Cost / number of units
Average price per unit = 140,000/200
Average price per unit = 700
b) Marginal Average Cost:
We know that marginal cost = [tex]C^{'}[/tex](x)
And the average marginal cost = [tex]\frac{d}{dx}[/tex] [tex]\frac{C(x)}{x}[/tex]
So,
= the derivative of ([tex]\frac{60,000 + 400(x)}{x}[/tex])
= the derivative of ([tex]\frac{(60,000)}{x} + 400[/tex])
= [tex]\frac{-60,000}{x^{2} }[/tex] + 0
So,
average marginal cost = [tex]\frac{-60,000}{x^{2} }[/tex]
at x = 200 units
average marginal cost = [tex]\frac{-60,000}{200^{2} }[/tex]
average marginal cost = -1.5 dollars/frame
c) Average cost per frame if 201 frames are produced:
We already seen in the part b that, the average marginal cost is decreasing by 1.5 dollars /frame. So,
if 201 frames are produced the instead of 200 then the difference is of 1 frame and we discussed that average marginal cost of 1 frame is decreasing at 1.5 dollars per frame.
So,
As we know the average cost from part a = 700 dollars.
Therefore, for 201 item = 700 dollars -1.5 dollars
For 201 frames are produced = $698.5
