Numerical Methods and Optimization

226 Numerical Methods and Optimization: An Introduction

it is obvious that this point (denoted by x

∗

inthefigure)isontheinter-

section of the lines defining the budget constraint (4x

1

+5x

2

=2, 000) and

the printed fabric constraint (x

2

= 300). Hence, we can find it by solving

the linear system consisting of these two equations. Solving this system gives

the optimal solution, x

∗

1

= 125,x

∗

2

= 300, which yields the optimal profit

z

∗

= $15 · 125 + $25 · 300 = $9, 375.

Example 10.8 Consider again the Heavenly Pouch example discussed in Sec-

tion 10.1 and just solved graphically. Suppose that the price of a non-reversible

carrier is raised by $5, so the new objective function is z =20x

1

+25x

2

.Solve

the resulting modified Heavenly Pouch LP graphically.

The modified Heav ...