The total cost (in dollars) of manufacturing x auto body frames is C(x)equals80 comma 000 plus 600 x. (A) Find the average cost per unit if 80 frames are produced. (B) Find the marginal average cost at a production level of 80 units. (C) Use the results from parts (A) and (B) to estimate the average cost per frame if 81 frames are produced.
Accepted Solution
A:
Answer: A) $1600, B) -$12.5, C) $1587.5.Step-by-step explanation:Since we have given that Total cost of manufacturing x auto body frames is given by[tex]C(x)=80000+600x[/tex](A) Find the average cost per unit if 80 frames are produced.Average cost is given by[tex]Average\ cost=\dfrac{80000+600x}{x}\\\\Average\ cost=\dfrac{80000}{x}+600=\dfrac{80000}{80}+600=1000+600=1600[/tex] (B) Find the marginal average cost at a production level of 80 units.[tex]A(x)=\dfrac{80000}{x}+600\\\\A'(x)=-80000x^{-2}\\\\A'(80)=-\dfrac{80000}{6400}\\\\A'(80)=-12.5[/tex] (C) Use the results from parts (A) and (B) to estimate the average cost per frame if 81 frames are produced.Average cost of 80 frames = $ 1600Marginal cost of 80 frames = -$12.5So, Average cost of 81 frames would be [tex]1600-12.5\\\\=\$1587.5[/tex]Hence, A) $1600, B) -$12.5, C) $1587.5.