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Find the graphical solution for the system of linear inequation 2x + y ≤ 2, x − y ≤ 1 - Mathematics and Statistics

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प्रश्न

Find the graphical solution for the system of linear inequation 2x + y ≤ 2, x − y ≤ 1

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उत्तर

To find graphical solution, construct the table as follows:

Inequation Equation Double intercept 
form
Points
(x, y)
Region
2x + y ≤ 2 2x + y = 2 `x/1 + y/2` = 1 A(1, 0)
B(0, 2)

2(0) + 0 ≤ 2
∴ 0 ≤ 2

∴ origin side

x − y ≤ 1 x − y = 1 `x/1 + y/(-1)` = 1 A(1, 0)
C(0, −1)

0 - 0 ≤ 1
∴ 0 ≤ 1

∴ origin side

The shaded portion represents the graphical solution.

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अध्याय 1.7: Linear Programming Problems - Short Answers I

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\[\text{Maximize}\text{ Z }= 3 x_1 + 5 x_2 \]
\[\text{ Subject }  to \text{ 3 } x_1 + 2 x_2 \leq 18\]
\[ x_1 \leq 4\]
\[ x_2 \leq 6\]
\[ x_1 \geq 0, x_2 \geq 0, \text{ is } \]

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A linear programming problem is given by Z = px + qy, where p, q > 0 subject to the constraints x + y ≤ 60, 5x + y ≤ 100, x ≥ 0 and y ≥ 0.

  1. Solve graphically to find the corner points of the feasible region.
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