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Linear Programming — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsLinear Programming5 Marks
Question
Solve the following linear programming problem graphically:
Maximise Z = 7x + 10y
subject to the constraints
4x + 6y $\leq$ 240
6x + 3y $\leq$ 240
x $\geq$ 10
x $\geq$ 0, y $\geq$ 0
✓

Answer


Maximise z = 7x + 10y, subject to 4x + 6y $\leq$ 240;
6x + 3y $\leq$ 240; x $\geq$ 10, x $\geq$ 0, y $\geq$ 0
Correct graph of three lines
For correct shading
$\text{Z}(\text{A})=\text{Z}\Big(10,\frac{200}{6}\Big)=70+10\times\frac{100}{3}=403\frac{1}{3}$
Z(B) = Z(30, 20) = 210 + 200 = 410
Z(C) = Z(40, 0) = 280 + 0 = 280
Z(D) = Z(10, 0) = 70 + 0 = 70
⇒ Max (= 410) at x = 30, y = 20

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