Chapter 11, Problem 30P

a

Summary Introduction

Interpretation: Number of workers to be hired and duration to hire.

Concept Introduction: Inventory management is the process of managing the company’s stock so that there are no stock-outs. It includes ordering, storing, and managing the stock.

Explanation of Solution

Required unit of production = 2,000,000

Number of workers employed = 500

Time required to assemble one unit = 3 minutes

  $\begin{array}{l}\mathrm{W}\mathrm{o}\mathrm{r}\mathrm{k}\mathrm{e}\mathrm{r}\mathrm{s}\text{'}\mathrm{p}\mathrm{r}\mathrm{o}\mathrm{d}\mathrm{u}\mathrm{c}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n}\mathrm{r}\mathrm{a}\mathrm{t}\mathrm{e}=\frac{60}{3}=20\mathrm{u}\mathrm{n}\mathrm{i}\mathrm{t}\mathrm{s}\mathrm{p}\mathrm{e}\mathrm{r}\mathrm{h}\mathrm{o}\mathrm{u}\mathrm{r}\\ \mathrm{M}\mathrm{o}\mathrm{n}\mathrm{t}\mathrm{h}\mathrm{l}\mathrm{y}\mathrm{c}\mathrm{a}\mathrm{p}\mathrm{a}\mathrm{c}\mathrm{i}\mathrm{t}\mathrm{y}=160\times 20=3,200\mathrm{u}\mathrm{n}\mathrm{i}\mathrm{t}\mathrm{s}\end{array}$

Capacity needed to produce 2000000 units, which is planned.

  $=\frac{2,000,000}{3,200}=625$

Since 500 workers are presently available, Number of workers to be hired is 125.

Month	Aug	Sept	Oct	Nov	Dec
Demand	1,000,000	1,000,000	2,000,000	4,000,000	1,000,000
Production plan	2,000,000	2,000,000	2,000,000	2,000,000	2,000,000
Beginning inventory	0	1,000,000	2,000,000	2,000,000	0
Ending inventory	1,000,000	2,000,000	2,000,000	0	1,000,000
Average inventory	500,000	1,500,000	2,000,000	1,000,000	500,000

b

Summary Introduction

Interpretation: Quantity of inventory at the end of October.

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

Explanation of Solution

The given schedule is calculated in ‘a’ part which shows inventory at the end of October will be 2 million when 125 workers are hired.

Month	Aug	Sept	Oct	Nov	Dec
Demand	1,000,000	1,000,000	2,000,000	4,000,000	1,000,000
Production plan	2,000,000	2,000,000	2,000,000	2,000,000	2,000,000
Beginning inventory	0	1,000,000	2,000,000	2,000,000	0
Ending inventory	1,000,000	2,000,000	2,000,000	0	1,000,000
Average inventory	500,000	1,500,000	2,000,000	1,000,000	500,000

At the end of October, 2 million inventory will be held.

c

Summary Introduction

Interpretation: Average inventory level of each month.

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

Explanation of Solution

Average inventory for august month:

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

  $\text{=}\frac{\text{0+}1\mathrm{M}}{\text{2}}=0.5\mathrm{M}$

Average inventory for September month:

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

  $\text{=}\frac{\text{+}1\mathrm{M}+2\mathrm{M}}{\text{2}}=1.5\mathrm{M}$

Average inventory for October month:

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

  $\text{=}\frac{2\mathrm{M}+2\mathrm{M}}{\text{2}}=2\mathrm{M}$

Average inventory for November month:

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

  $\text{=}\frac{2\mathrm{M}+0}{\text{2}}=1\mathrm{M}$

Average inventory for December month:

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

  $\text{=}\frac{0+1}{\text{2}}=0.5\mathrm{M}$

Note: M stands for millions.