Operations and Supply Chain Management (Mcgraw-hill Education)
Operations and Supply Chain Management (Mcgraw-hill Education)
15th Edition
ISBN: 9781259666100
Author: F. Robert Jacobs, Richard B Chase
Publisher: McGraw-Hill Education
Question
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Chapter 7, Problem 12OQ

a)

Summary Introduction

To calculate: The break-even point in dollars of sales and in chairs and bar stools when the sales mix is 1:1.

Break-even point:

It is the point in a business at which the total costs and total revenues are equal. It is the position after which the firm begins to see profits.

a)

Expert Solution
Check Mark

Explanation of Solution

Given information:

Fixed cost (FC)     = $20,000

Chairs (c):

Price (P)         = $50

Variable cost (VC)     = $25

Bar stools (b):

Price (P)         = $50

Variable cost (VC)     = $20

Calculation of break-even point in chairs and stools:

Let FC be the fixed cost.Let Pi be the price for product 'i'.Let VCi be the variable cost for product 'i'.Let Vi be the volume for product 'i'.Where 'i' is the chair(c) and bar stool (b).

FC=((Pc-VCc)×Vc)+((Pb-VCb)×Vb)20,000=((50-25)×V)+((50-20)×V)[Since, V=Vc=Vb]20,000=25V+30VV=20,00055=364 chairs and bar stools.

Calculation of break-even point in dollars:

BEPdollars=(Cost of chair×Number of units)+(Cost of bar stool×Number of units)=($50×364)+($50×364)=18,200+18,200=$36,400

b)

Summary Introduction

To calculate: The break-even point in dollars of sales and in chairs and bar stools when the sales mix is 1:4.

b)

Expert Solution
Check Mark

Explanation of Solution

Given information:

Fixed cost (FC)     = $20,000

Chairs (c):

Price (P)         = $50

Variable cost (VC)     = $25

Bar stools (b):

Price (P)         = $50

Variable cost (VC)     = $20

Calculation of break-even point in chairs and stools:

Let FC be the fixed cost.Let Pi be the price for product 'i'.Let VCi be the variable cost for product 'i'.Let Vi be the volume for product 'i'.Where 'i' is the chair(c) and bar stool (b).

FC=((Pc-VCc)×Vc)+((Pb-VCb)×Vb)20,000=((50-25)×V)+((50-20)×4V)[Since, V=Vc=0.25Vb]20,000=25V+120VVChairs=20,000145=138 chairsVBar stools=138×4=552 bar stools

Calculation of break-even point in dollars:

BEPdollars=(Cost of chair×Number of units)+(Cost of bar stool×Number of units)=($50×138)+($50×552)=6,900+27,600=$34,500

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