Chapter 11, Problem 29P

a

Summary Introduction

Interpretation: Number of bows at the end of fourth month is to be calculated.

Concept Introduction: Weighted average method is the method in which different numerical value is given to variable depending upon its importance. Higher the importance, larger is the numerical value given.

Explanation of Solution

All figures are in ‘000.

For month 1:

Calculation of average inventory::

  $\text{Average}\text{inventory}\text{=}{\text{(B}}_{\text{i}}\text{+}{\text{E}}_{\text{i}}\text{)/2}$

Where,

  ${\text{B}}_{\text{i}}$ = beginning inventory

  ${\text{E}}_{\text{i}}$ = ending inventory

  $\begin{array}{l}\text{Total}\text{inventory}\text{cost}\text{=}\text{\$1×}\text{total}\text{inventory}\text{for}\text{4}\text{months}\\ \text{=}\text{\$1}\text{×}\text{(15+35+5)}\text{×}\text{1000}\\ \text{=}\text{85000}\end{array}$

Where,

  $P_{\text{i}}$ = Production during month

  $D_{\text{i}}$ = Demand during month

  $\begin{array}{l}{A}_1=(0+15)/2\\ =7.5\end{array}$

Average inventory for 1^st moth is 7500.

For month 2:

Calculation of average inventory::

  $\text{Average}\text{inventory}\text{=}{\text{(B}}_{\text{i}}\text{+}{\text{E}}_{\text{i}}\text{)/2}$

Where,

  ${\text{B}}_{\text{i}}$ = beginning inventory

  ${\text{E}}_{\text{i}}$ = ending inventory

  $\begin{array}{l}{\text{B}}_2=15\\ E_2={\text{B}}_{\text{i}}+P_{\text{i}}-D_{\text{i}}\\ E_{\text{i}}=15+25-5=35\end{array}$

Where,

  $P_{\text{i}}$ = Production during month

  $D_{\text{i}}$ = Demand during month

  $\begin{array}{l}{A}_2=(15+35)/2\\ =25\end{array}$

Average inventory for 2^nd month is25000.

For month 3:

Calculation of average inventory::

  $\text{Average}\text{inventory}\text{=}{\text{(B}}_{\text{i}}\text{+}{\text{E}}_{\text{i}}\text{)/2}$

Where,

  ${\text{B}}_{\text{i}}$ = beginning inventory

  ${\text{E}}_{\text{i}}$ = ending inventory

  $\begin{array}{l}{\text{B}}_3=35\\ E_3={\text{B}}_3+P_3-D_3\\ E_3=35+25-30=30\end{array}$

Where,

  $P_{\text{i}}$ = Production during month

  $D_{\text{i}}$ = Demand during month

  $\begin{array}{l}{A}_3=(15+35)/2\\ =32.5\end{array}$

Average inventory for 3rd month is 32500.

For month 4:

Calculation of average inventory::

  $\text{Average}\text{inventory}\text{=}{\text{(B}}_{\text{i}}\text{+}{\text{E}}_{\text{i}}\text{)/2}$

Where,

  ${\text{B}}_{\text{i}}$ = beginning inventory

  ${\text{E}}_{\text{i}}$ = ending inventory

  $\begin{array}{l}{\text{B}}_4=0\\ E_4={\text{B}}_{\text{i}}+P_{\text{i}}-D_{\text{i}}\\ E_{\text{4}}=30+25-50=5\end{array}$

Where,

  $P_{\text{i}}$ = Production during month

  $D_{\text{i}}$ = Demand during month

  $\begin{array}{l}{A}_4=(30+5)/2\\ =32.5\end{array}$

Average inventory for 2^nd month is 32500.

Number of bows at the end of the month is 5000

b

Summary Introduction

Interpretation: The month that has the highest inventory is to be determined.

Concept Introduction: Weighted average method is the method in which different numerical value is given to variable depending upon its importance. Higher the importance, larger is the numerical value given.

Explanation of Solution

  $\begin{array}{l}{E}_4={\text{B}}_{\text{i}}+P_{\text{i}}-D_{\text{i}}\\ E_{\text{4}}=30+25-50=5\end{array}$

Fouth month has the highest inventory as ending inventory is 5000.

c

Summary Introduction

Interpretation: Total inventory cost is to be calculated.

Concept Introduction: Holding cost or inventory cost is the cost of warehousing in which unsold goods are kept. It includes transportation, warehousing, insurance etc.

Explanation of Solution

Cost of inventory = $1 per unit.

  $\begin{array}{l}\text{Total}\text{inventory}\text{cost}\text{=}\text{\$1×}\text{total}\text{inventory}\text{for}\text{4}\text{months}\\ \text{=}\text{\$1}\text{×}\text{(15+35+5)}\text{×}\text{1000}\\ \text{=}\text{85000}\end{array}$

Total inventory cost is $85000