Question

exercises 1.4 integration formulas and the net change theorem
score: 80/140 answered: 9/14
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question 10
the marginal cost for printing a paperback book at a small publishing company is
c(p) = $0.02 per page where p is the number of pages in the book
a 720 page book has a $20.77 production cost. find the production cost function c(p).
c(p) = $
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Explanation:

Step1: Integrate marginal cost

$C(p) = \int 0.02 dp = 0.02p + K$

Step2: Solve for constant K

Substitute $p=720, C(720)=20.77$:
$20.77 = 0.02(720) + K$
$20.77 = 14.4 + K$
$K = 20.77 - 14.4 = 5.37$

Step3: Write cost function

$C(p) = 0.02p + 5.37$

Answer:

$C(p) = 0.02p + 5.37$