(a.)
The quantity that will minimize
(a.)
Answer to Problem 60E
It has been determined that the quantity that will minimize
Explanation of Solution
Given:
The average weekly cost of ordering, paying for, and holding merchandise is,
Here,
Concept used:
A function attains its minimum value at a point for which the first derivative of the function is zero and the second derivative of the function is positive.
Calculation:
It is given that
Differentiating with respect to
Differentiating again with respect to
Equating first derivative to zero,
Simplifying,
On further simplification,
Solving,
Now,
Considering the positive root only,
Put
Note that the above quantity is positive because
So, the quantity that will minimize
Conclusion:
It has been determined that the quantity that will minimize
(b.)
The most economical quantity to order when
(b.)
Answer to Problem 60E
It has been determined that the most economical quantity to order, when
Explanation of Solution
Given:
The average weekly cost of ordering, paying for, and holding merchandise is,
Here,
Concept used:
A function attains its minimum value at a point for which the first derivative of the function is zero and the second derivative of the function is positive.
Calculation:
It is given that
Replacing
Simplifying,
Differentiating with respect to
Differentiating again with respect to
Equating first derivative to zero,
Simplifying,
On further simplification,
Solving,
Now,
Considering the positive root only,
Put
Note that the above quantity is positive because
So, the quantity that will minimize
Thus, the most economical quantity to order, when
Conclusion:
It has been determined that the most economical quantity to order, when
Chapter 4 Solutions
AP CALCULUS TEST PREP-WORKBOOK
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