Concept explainers
To calculate:the Rich’s average daily inventory and average daily holding cost.
Answer to Problem 44RE
The value is
Explanation of Solution
Given information:
The Rich Wholesale Foods, a manufacturer of cookies, stores its cases of cookies in an air-conditioned warehouse for shipment every 14 days. Rich tries to keep 600 cases on reserve to meet occasional peaks in demand, so a typical 14-day inventory function is
Formula used:
Calculation:
Calculate, Rich’s average daily inventory by using average formula
Now, calculate the value of integral
If f is continuous at every point of [a, b], and if F is any anti-derivative of f on [a, b], then
This part of the fundamental theorem is also called the integral evaluation theorem.
Proof
Part 1 of the fundamental theorem tells us that an anti-derivative of f exists, namely
Thus, if F is any anti- derivative of f , then
So,
Now, use the above proof to find the value of integral.
If F is any anti-derivative of f, then
So,
Now, calculate the value of average
Since, holding cost for each case is 4¢. Thus, holding cost is given by
Now, take average both sides
This part of the fundamental theorem is also called the integral evaluation theorem.
Proof:
Part 1 of the fundamental theorem tells us that an anti-derivative or f exists, namely
Thus, if F is any anti-derivative of f , then
So,
Now, use the above proof to find the value of integral.
If F is any anti-derivative of f , then
So,
Now, calculate the value of average
Conclusion:
The value is
Chapter 6 Solutions
Calculus: Graphical, Numerical, Algebraic
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