A company anticipates there will be a demand for 20,000 copies of a certain book during the next year/. It costs the company $0.50 to store a book for 1 year. Each time it must print additional books, it costs $200 to set up the equipment. NOTE: We assume that the demand is uniform. Let x= number of books printed during each printing run y= number of printing runs Use this information to answer questions 1-6 below 1) Since x is the number of books printed in each printing run, x must satisfy 1 ≤ x ≤_____. In other words, x is in the closed interval [a,b], where a =1 and b = _______. 2) Using the calculations above, we can express the total cost C(x) as a function of x, with the restriction on x given in the previous problem. Find the critical number of C(x) by solving C′(x)=0. NOTE: Because of the restriction on x, there is exactly one critical number c. 3) There is only one critical number c in the interval, and the cost function C(x) is continuous. Since C′(c) _______________ and C″(c) _________ we can use the ___________to conclude that C(c) is the ___________________ of the cost function on the interval I. 4) How many books should be produced during each printing run to minimize total cost? ___________ books 5)How many printing runs should be done? __________printing runs 6) What is the minimum total cost? $_______
A company anticipates there will be a demand for 20,000 copies of a certain book during the next year/. It costs the company $0.50 to store a book for 1 year. Each time it must print additional books, it costs $200 to set up the equipment.
NOTE: We assume that the demand is uniform.
Let
- x= number of books printed during each printing run
- y= number of printing runs
Use this information to answer questions 1-6 below
1) Since x is the number of books printed in each printing run, x must satisfy 1 ≤ x ≤_____.
In other words, x is in the closed interval [a,b], where a =1 and b = _______.
2) Using the calculations above, we can express the total cost C(x) as a function of x, with the restriction on x given in the previous problem.
Find the critical number of C(x) by solving C′(x)=0.
NOTE: Because of the restriction on x, there is exactly one critical number c.
3) There is only one critical number c in the interval, and the cost function C(x) is continuous.
Since C′(c) _______________ and C″(c) _________ we can use the ___________to conclude that C(c) is the ___________________ of the cost function on the interval I.
4) How many books should be produced during each printing run to minimize total cost?
___________ books
5)How many printing runs should be done?
__________printing runs
6) What is the minimum total cost?
$_______
Trending now
This is a popular solution!
Step by step
Solved in 2 steps with 5 images
