Explanation Given information: The products are Alpha 1 model robots and Beta 2 model robots. Number of technicians are 5. Number of working hours per month is 160 hours Alpha 1 model robots Beta 2 model robots Labor hours 20 25 Minimum number of robots 10 15 Profit($) 1,200 1,800 Calculation of total available hours: Total available hours = Number of technicians × Number of working hours per month = 5 × 160 = 800 hours Let ‘ x 1 ’ be the number of Alpha 1 model robots . Let ‘ x 2 ’ be the number of Beta 2 model robots . Formulation: Maximize = 1 , 200 x 1 + 1 , 800 x 2 ( Profit ) Subject to: 20 x 1 + 25 x 2 ≤ 800 ( Available hours ) x 1 ≥ 10 ( Minimum Alpha1 robots ) x 2 ≥ 15 ( Minimum Beta 2 robots ) x 1 , x 2 ≥ 0 ( Non-negativity ) Calculation of (x1, x2) coordinates for each constraint: Constraint 1: 20 x 1 + 25 x 2 ≤ 800 To determine the ‘x1’ coordinate, the value of ‘x2’ is substituted with ‘0’ and equated with the right-hand side value. 20 x 1 + 25 ( 0 ) = 800 20 x 1 = 800 x 1 = 800 20 x 1 = 40 To determine the ‘x2’ coordinate, the value of ‘x1’ is substituted with ‘0’ and equated with the right-hand side value

Operations Management 11/e (2 Colors) By Heizer (2015-12-25)

11th Edition

ISBN: 9789332548985

Author: HEIZER

Publisher: Pearson India

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Optimization Models

Optimization models are mathematical models that help organizations determine the best way to allocate scarce resources to achieve specific objectives. These models can be used to solve a wide variety of problems, from finding the most efficient route fo…

Question

Chapter B, Problem 10P

Summary Introduction

To determine: The best profitable mix of robots using linear programming.

Introduction:

Linear programming:

It is a linear optimization technique followed to develop the best outcome for the linear programming problem. The outcome might be to maximize profit, minimize cost, or to determine the optimal product mix. The outcome will take the constraints present in achieving the solution into consideration.

Expert Solution & Answer

Chapter B Solutions

Operations Management 11/e (2 Colors) By Heizer (2015-12-25)

Ch. B - Prob. 1DQ Ch. B - Prob. 2DQ Ch. B - Prob. 3DQ Ch. B - Prob. 4DQ Ch. B - Prob. 5DQ Ch. B - Prob. 6DQ Ch. B - Prob. 7DQ Ch. B - Prob. 8DQ Ch. B - Prob. 9DQ Ch. B - Prob. 10DQ

Ch. B - Prob. 11DQ Ch. B - Where a constraint crosses the vertical or...Ch. B - Prob. 13DQ Ch. B - Prob. 1P Ch. B - Prob. 2P Ch. B - Prob. 3P Ch. B - B.4. Consider the following linear programming...Ch. B - Prob. 5P Ch. B - Prob. 6P Ch. B - Prob. 7P Ch. B - Prob. 8P Ch. B - Green Vehicle Inc. manufactures electric cars and...Ch. B - Prob. 10P Ch. B - Prob. 11P Ch. B - Prob. 12P Ch. B - The LP relationships that follow were formulated...Ch. B - Prob. 14P Ch. B - Prob. 15P Ch. B - Prob. 16P Ch. B - Prob. 17P Ch. B - Prob. 18P Ch. B - Prob. 19P Ch. B - Prob. 20P Ch. B - Prob. 21P Ch. B - Prob. 22P Ch. B - Prob. 23P Ch. B - How many corner points are there in the feasible...Ch. B - Prob. 25P Ch. B - Prob. 26P Ch. B - A fertilizer manufacturer has to fulfill supply...Ch. B - Prob. 28P Ch. B - Bowman Builders manufactures steel storage sheds...Ch. B - Prob. 30P Ch. B - Quain Lawn and Garden, Inc Bill and Jeanne Quain...Ch. B - Quain Lawn and Garden, Inc Bill and Jeanne Quain...

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Solution Summary: The author explains linear programming as a linear optimization technique used to determine the best profitable mix of robots.

Concept explainers

Chapter B Solutions