Page 239 - How To Solve Word Problems In Calculus

We reject the negative solution.Since the profit function is
continuous on the closed interval [0, 30], we compare the value of
P (x)at x = 20 with its values at the interval endpoints.

P (0) =−40 P (20) = 920 P (30) = 380
The maximum profit occurs when 20 cameras are sold daily.
10. This is an inventory problem.We let x represent the size of each
printing in units of 1000 books.The storage (holding) cost is

x
H(x) = (annual storage cost per item)
2

x
= 600
2
= 300x
The ordering cost is
O(x) = (cost per printing)(number of printings)

q
= (cost per printing)
x
Remember, q is in thousands.
200
= (3750)
x
= 750,000x −1
The total printing cost, $3 × 200,000 = $600,000 can be ignored
(see note on page 218).
C (x) = H(x) + O(x)
= 300x + 750,000x −1

C (x) = 300 − 750,000x −2
750,000
0 = 300 −
x 2
750,000
= 300
x 2
2
300x = 750,000
2
x = 2500
x = 50
To minimize cost, each printing should be 50,000 copies.

226