Chapter 3.1, Problem 2P

a.

Program Plan Intro

Feasible region:

A feasible region for an LPP is the set of all points that satisfies the constraints and non-negative restrictions of the corresponding LPP.

Mathematical model of the given LPP:

$\text{Maximize}{\text{z = 30x}}_{\text{1}}{\text{+100x}}_{\text{2}}$

Subject to the constraints,

$\begin{array}{l}{\text{x}}_{\text{1}}{\text{+x}}_{\text{2}}\le \text{7(Land constraints)}\\ {\text{4x}}_{\text{1}}{\text{+10x}}_{\text{2}}\le \text{40(Labor constraint)}\\ {\text{10x}}_{\text{1}}\ge \text{30}\text{(Government constraint)}\\ {\text{x}}_{\text{1}}{\text{,x}}_{\text{2}}\ge \text{0(Sign restriction)}\end{array}$

b.

Explanation of Solution

Determining feasible region:

Given point: $(x_1=4,x_2=3)$

The points $x_1$ and $x_2$ are positive, non-negative restriction is satisfied. Substituting the point values in the constraints to check the given inequalities are satisfied

c.

Explanation of Solution

Determining feasible region:

Given point: $(x_1=2,x_2=-3)$

d.

Explanation of Solution

Determining feasible region:

Given point: $(x_1=3,x_2=2)$

The points $x_1$ and $x_2$ are positive, non-negative restriction is satisfied. Substituting the point values in the constraints to check the given inequalities are satisfied