Chapter 11, Problem 27P

Summary Introduction

Interpretation: The percentage change in the average inventory between October and November is to be calculated.

Concept Introduction: Materials Requirement Planning is a process in which planning is made for the requirement of raw material required foe manufacturing of finished product.

Aggregate planning is a marketing process in which production of output is planes in advance for some months to give an idea to management regarding procurement of goods.

Explanation of Solution

It is given that the beginning inventory of October is 300 tons and the ending inventory of October is 100 tons. Ending inventory of the month is the beginning inventory of the month of November.

It is calculated by taking the average of beginning inventory and ending inventory of the month of October.

  $\text{Average}\text{inventory}\text{=}\frac{\text{Beginning}\text{inventory}\text{+Ending}\text{inventory}}{\text{2}}$

  $\begin{array}{l}\text{Average}\text{inventory}\text{=}\frac{\text{300}\text{tons+100}\text{tons}}{\text{2}}\\ \text{=}\text{200}\text{tons}\end{array}$

Hence, the average inventory for the month of October is 200 tons.

Calculation of average inventory for the month of November:

  $\text{Average}\text{inventory}\text{=}\frac{\text{Beginning}\text{inventory}\text{+Ending}\text{inventory}}{\text{2}}$

  $\begin{array}{l}\text{Average}\text{inventory}\text{=}\frac{\text{100}\text{tons+200}\text{tons}}{\text{2}}\\ \text{=}15\text{0}\text{tons}\end{array}$

Hence, the average inventory for the month of November is 150 tons.

Calculation of percentage change in the average inventory between October and November:

It is calculated by dividing the value attained by subtracting the value 1 from value 2 with the value 1. Then, multiply the attained value with 100 to find the percentage.

  $\begin{array}{l}\text{Percentage}\text{change}\text{=}\left(\frac{\text{Value}\text{2}\text{-}\text{Value}\text{1}}{\text{Value}\text{1}}\right)\text{×}\text{100}\\ \text{=}\left(\frac{\text{150}\text{tons}\text{-}\text{200}\text{tons}}{\text{200}\text{tons}}\right)\text{×}\text{100}\\ \text{=}\frac{\text{-150}\text{tons}}{\text{200}\text{tons}}\text{×}\text{100}\\ \text{=}\text{-0}\text{.25}\text{×}\text{100}\\ \text{=}\text{-25\%}\end{array}$

Hence, the percentage change in the average inventory between October and November is -25%.