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Linear Programming — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsLinear Programming5 Marks
Question
Maximize Z = 4x + 3y
Subject to
$3\text{x}+4\text{y}\leq24$
$8\text{x}+6\text{y}\leq48$
$\text{x}\leq5$
$\text{y}\leq5$
$\text{x},\text{y}\geq0$
✓

Answer


$\text{3x}+\text{4y }\leq24\ ;$ when x = 0, y = 6 & when y = 0, x = 8, line AB
$\text{8x}+\text{6y }\leq48\ ;$ when x = 0, y = 8 & when y = 0, x = 8, line CD
Plotting $\text{x}\leq5$ given line EF; Plotting $\text{y}\leq6$ given line AG
The feasible area is 0, 0 - C - H - G - E
Corner point Value of Z = 4x + 3y
0, 0 0
0, 6 18
3.4, 3.4 24
5, 1 23
5, 0 20
The maximum of Z = 4x + 3y, occurs at x = 3.4, y = 3.4

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