Answer to Question #190211 in Calculus for Ezekiel Morales

Question

Hands-On Calendar has found that the cost per card of producing x pocket calendar cards is given by

 C'(x) = -0.02x + 50, for x ≤ 800,

where c(x) is the cost, in cents, per card. Find the total cost, in dollars, of producing 550 cards.

Answer 1

 Ans:-

$C'(x) = -0.02x + 50,$ $for x ≤ 800$

integrating the above equation

$\Rightarrow \int C'(x)=\int-0.02x+50$

$\Rightarrow C(x)=-0.01x^2+50x$

to find the total cost, in dollars, of producing 550 cards then put $x=550$

$C(550)=-0.01(550)^2+50\times550=24475$ $