MHT CET · Maths · Linear Programming
The shaded area in the given figure is a solution set for some system of inequations. The maximum value of the function \(z=10 x+25 y\) subject to the linear constraints given by the system is
- A 80
- B 100
- C 95
- D 105
Answer & Solution
Correct Answer
(C) 95
Step-by-step Solution
Detailed explanation
\(\begin{aligned} & \text { At }(0,0), z=10(0)+25(0)=0 \\ & \text { At }(3,0), z=10(3)+25(0)=30 \\ & \text { At }(3,2), z=10(3)+25(2)=80 \\ & \text { At }(2,3), z=10(2)+25(3)=95 \\ & \text { At }(0,3), z=10(0)+25(3)=75\end{aligned}\)
\(\therefore \quad\) Maximum value of \(\mathrm{z}\) is 95 .
\(\therefore \quad\) Maximum value of \(\mathrm{z}\) is 95 .
See the Complete Solution
Get step-by-step explanations for this and 2.5 Lakh+ more JEE, NEET & CET questions.
- Unlock all solutions
- Practice the full chapter
- Track accuracy across PYQs
4.8 rated on Google Play · 14,000+ reviews
More questions from Maths
- \(\int \frac{e^x}{\left(2+e^x\right)\left(e^x+1\right)} d x=\)
(where \(C\) is \(a\) constant of integration.)MHT CET 2022 Easy - Equation of planes parallel to the plane \(x-2 y+2 z+4=0\) which are at a distance of one unit from the point \((1,2,3)\) areMHT CET 2021 Medium
- If \(x=t+\frac{1}{t}\) and \(y=t-\frac{1}{t}\), the \(\frac{\mathrm{d} y}{\mathrm{~d} x}=\)MHT CET 2022 Easy
- If \(y=\sqrt{e^{\sqrt{x}}}\), then \(\frac{d y}{d x}=\)MHT CET 2021 Easy
- A fair die with numbers 1 to 6 on their faces is thrown. Let \(\mathrm{X}\) denote the number of factors of the number, on the uppermost face, then the probability distribution of \(\mathrm{X}\) isMHT CET 2023 Easy
- If the equation \(k x y+5 x+3 y+2=0\) represents a pair of lines, then \(k=\)MHT CET 2020 Medium
More PYQs from MHT CET
- Calculate standard internal energy change for \(\mathrm{OF}_{2(\mathrm{~g})}+\mathrm{H}_2 \mathrm{O}_{(\mathrm{g})} \longrightarrow 2 \mathrm{HF}_{(\mathrm{g})}+\mathrm{O}_{2(\mathrm{~g})}\) at 300 K, if \(\Delta_{\mathrm{f}} \mathrm{H}^{\circ}\) of \(\mathrm{OF}_{2(\mathrm{~g})}, \mathrm{H}_2 \mathrm{O}_{(\mathrm{g})}\) and \(\mathrm{HF}_{(\mathrm{g})}\) are 20, -250 and \(\quad-270 \quad \mathrm{~kJ} \quad \mathrm{~mol}^{-1} \quad\) respectively. \(\left[\mathrm{R}=8.314 \mathrm{~J} \mathrm{~K}^{-1} \mathrm{~mol}^{-1}\right]\)MHT CET 2024 Medium
- An electron of mass ' \(m_e\) ' and a proton of mass ' \(m_p\) ' are kept in a uniform electric field. The ratio of the acceleration of electron \(\left(a_e\right)\) to the acceleration of proton \(\left(a_p\right)\) isMHT CET 2022 Easy
- Molecular evolution and origin of life occurred in ___________ era.MHT CET 2018 Hard
- The value of where are constants, depends only on ________MHT CET 2019 Medium
- The distance of a point \((1,2,-1)\) from the plane \(x-2 y+4 z+10=0\) isMHT CET 2020 Easy
- A pendulum bob has a speed \(4 \mathrm{~m} / \mathrm{s}\) at its lowest position. The pendulum is 1 m long. When the length of the string makes an angle of \(60^{\circ}\) with the vertical, the speed of the bob at that position is (acceleration due to gravity, \(g=10 \mathrm{~m} / \mathrm{s}^2, \cos 60^{\circ}=0 \cdot 5\) )MHT CET 2025 Medium