Introduction to Management Science (12th Edition)
Introduction to Management Science (12th Edition)
12th Edition
ISBN: 9780133778847
Author: Bernard W. Taylor III
Publisher: PEARSON
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Question
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Chapter 2, Problem 1P

a)

Summary Introduction

To formulate: A linear programming model for the given problem.

a)

Expert Solution
Check Mark

Explanation of Solution

Formulation:

Let x1 be the number of cakes.Let x2 be the number of loaves of bread.

Maximize Z=10x1+6x2Subject to:3x1+8x220cups of flour45x1+30x2180minutesx1,x20

b)

Summary Introduction

To solve: The problem graphically.

b)

Expert Solution
Check Mark

Explanation of Solution

Calculation of coordinates

Constraint 1:

30+8x2=20x2=208=2.5

3x1+80=20x1=203=6.67

The coordinates are (6.67, 2.5).

Constraint 2:

450+30x2=180x2=18030=6

45x1+300=180x1=18045=4

The coordinates are (4, 6).

Graph:

Introduction to Management Science (12th Edition), Chapter 2, Problem 1P , additional homework tip  1

The three corner points encompassing the feasible region are A (0, 2.5), B (3.111, 1.333), and C (4, 0).

Calculation of object function value:

Formulas:

Introduction to Management Science (12th Edition), Chapter 2, Problem 1P , additional homework tip  2

Answer:

Introduction to Management Science (12th Edition), Chapter 2, Problem 1P , additional homework tip  3

The optimal solution is:

Number of cakes = 4

Number of loaves of bread = 0

Value of the objective function = 40

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