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Solve the following system of inequalities graphically 3x + 2y ≤ 150, x + 4y ≥ 80, x ≤ 15, y ≥ 0, x ≥ 0 - Mathematics and Statistics

Graph

Solve the following system of inequalities graphically.
3x + 2y ≤ 150, x + 4y ≥ 80, x ≤ 15, y ≥ 0, x ≥ 0

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Solution

To find graphical solution, construct the table as follows:

Inequation Equation Doule Intercept form Points
(x, y)
Region
3x + 2y ≤ 150 3x + 2y = 150 `"x"/50 + "y"/75` = 1 A (50, 0),
B (0, 75)
3(0) + 2(0) ≤  150
∴ 0 ≤  150
∴ origin side
x + 4y ≥ 80 x + 4y = 80 `"x"/80 + "y"/20` = 1 C (80, 0),
D (0, 20)
0 + 4(0) `≱` 80
∴ 0 `≱` 80
∴ non-origin side
x ≤ 15 x = 15 0 ≤ 15
∴ L.H.S. of the line
x = 15
x ≥ 0 x = 0 R.H.S. of Y-axis
y ≥ 0 y = 0 Above X-axis


The shaded portion represents the graphical solution.

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APPEARS IN

Balbharati Mathematics and Statistics 2 (Commerce) 11th Standard HSC Maharashtra State Board
Chapter 8 Linear Inequations
Miscellaneous Exercise 8 | Q 14 | Page 122
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