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Fisher Company produces two types of components for airplanes: A and B, with unit contribution margins of $400 and $600, respectively. The components pass through three sequential processes: cutting, welding, and assembly. Data pertaining to these processes and market demand are given below (weekly data). Required: 1. Express Fisher Company’s constrained optimization problem as a linear programming model. 2. Using a graphical approach, solve the linear programming model expressed in Requirement 1. Which constraints are binding? 3. What if Fisher Company had 10 additional machine hours (cutting) with all other resources held constant? What is the new optimal mix and associated total contribution margin? What is the incremental benefit per machine hour caused by the additional five hours, if any?

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Cornerstones of Cost Management (C...

4th Edition
Don R. Hansen + 1 other
Publisher: Cengage Learning
ISBN: 9781305970663

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Section
BuyFindarrow_forward

Cornerstones of Cost Management (C...

4th Edition
Don R. Hansen + 1 other
Publisher: Cengage Learning
ISBN: 9781305970663
Chapter 20, Problem 4CE
Textbook Problem
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Fisher Company produces two types of components for airplanes: A and B, with unit contribution margins of $400 and $600, respectively. The components pass through three sequential processes: cutting, welding, and assembly. Data pertaining to these processes and market demand are given below (weekly data).

Chapter 20, Problem 4CE, Fisher Company produces two types of components for airplanes: A and B, with unit contribution

Required:

  1. 1. Express Fisher Company’s constrained optimization problem as a linear programming model.
  2. 2. Using a graphical approach, solve the linear programming model expressed in Requirement 1. Which constraints are binding?
  3. 3. What if Fisher Company had 10 additional machine hours (cutting) with all other resources held constant? What is the new optimal mix and associated total contribution margin? What is the incremental benefit per machine hour caused by the additional five hours, if any?

1.

To determine

Prepare Company F’s constrained optimization problem as a linear programming model.

Explanation of Solution

Theory of constraint: Making money in the future by managing constraints is the main goal of the theory of constraints. The theory of constraints (TOC) recognizes the performance of origination with constraints volume and it develops a specific approach to focus the system level effects of the continuous improvement.

Prepare Company F’s constrained optimization problem as a linear programming model as follows:

Maz Z=$400 A+$600 B

Internal constraints:

Maz Z=6 A+10 B300  (cutting)=10A

2.

To determine

Draw a graph for the linear programming model expressed in Requirement 1 and state the constraints that are binding.

3.

To determine

Ascertain the new optimal mix and the total contribution margin. State the incremental benefit per machine hour caused by the additional five hours.

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Chapter 20 Solutions

Cornerstones of Cost Management (Cornerstones Series)
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