Question

Convert the following problems to standard form

minimize x+2y+3z,
subject to 2<=x+y<=3§,
4<=y+z<=5
x>=0, y>=0, z>=0.
(b.)x+y+z,
subject to x+2y+3z=10,
x>=1, y>=2, z>=1

Answer 1

To convert the given problems to standard form, you rewrite the inequalities and equations in a specific format. Problem (a) is to minimize x+2y+3z, subject to 2<=x+y<=3 and 4<=y+z<=5, with constraints x>=0, y>=0, z>=0. Problem (b) is to minimize x+y+z, subject to x+2y+3z=10, with constraints x>=1, y>=2, z>=1.

Step-by-step explanation:

To convert the given problems to standard form, you need to rewrite the inequalities and equations in a specific format. Let's start with problem (a): minimize x+2y+3z, subject to 2<=x+y<=3 and 4<=y+z<=5, with the constraints x>=0, y>=0, z>=0. To convert this to standard form, we rewrite the inequalities in equation form and introduce slack variables:

1. x+y+s1=3
2. -x-y+s2=2
3. y+z+s3=5
4. -y-z+s4=4

Problem (b) is to minimize x+y+z, subject to x+2y+3z=10, with the constraints x>=1, y>=2, z>=1. To convert this to standard form, we introduce slack variables and rewrite the equation and constraints:

1. x+2y+3z+s1=10
2. x>=1
3. y>=2
4. z>=1