MHT CET · Maths · Linear Programming
The maximum value of the objective function \(\mathrm{z}=4 x+6 y\) subject to \(3 x+2 y \leq 12, x+y \geq 4, x\), \(y \geq 0\) is
- A 24
- B 46
- C 56
- D 36
Answer & Solution
Correct Answer
(D) 36
Step-by-step Solution
Detailed explanation
The corner points of feasible region are \(\mathrm{A}(4,0)\), \(\mathrm{B}(0,4), \mathrm{C}(0,6)\)
At \(A(4,0), Z=4(4)+6(0)=16\)
At B( 0,4\(), Z=4(0)+6(4)=24\)
At \(\mathrm{C}(0,6), \mathrm{Z}=4(0)+6(6)=36\)
\(\therefore \quad \mathrm{Z}\) has maximum value at \(\mathrm{C}(0,6)\) which is 36 .
At \(A(4,0), Z=4(4)+6(0)=16\)
At B( 0,4\(), Z=4(0)+6(4)=24\)
At \(\mathrm{C}(0,6), \mathrm{Z}=4(0)+6(6)=36\)
\(\therefore \quad \mathrm{Z}\) has maximum value at \(\mathrm{C}(0,6)\) which is 36 .
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
- \(\int_{0}^{\frac{\pi}{2}} \frac{\sqrt[7]{\sin x}}{\sqrt[7]{\sin x}+\sqrt[7]{\cos x}} d x=\)MHT CET 2020 Easy
- If \(\mathrm{A}=(-2,2,3), \mathrm{B}=(3,2,2), \mathrm{C}=(4,-3,5)\) and \(\mathrm{D}=(7,-5,-1)\) Then the projection of \(\overline{\mathrm{AB}}\) on \(\overline{\mathrm{CD}}\) isMHT CET 2021 Easy
- Let \(S\) be a non-empty subset of \(\mathbb{R}\). Consider the following statement:
p : There is a rational number \(x \in \mathrm{~S}\) such that \(x\gt0\).
Which of the following statements is the negation of the statement p?MHT CET 2024 Medium - The slope of the tangent at \((x, y)\) to the curve passing through \((2,1)\) is \(\frac{x^2+y^2}{2 x y}\), then the equation of the curve isMHT CET 2025 Medium
- If \(\mathrm{f}(x)=(1+x)\left(1+x^2\right)\left(1+x^4\right)\left(1+x^8\right)\), then \(f^{\prime}(1)=\)MHT CET 2024 Medium
- If the sum of the deviations of 50 observations from 30 is 50 , then the mean of these observations isMHT CET 2024 Easy
More PYQs from MHT CET
- \(\bar{a}=\hat{i}+\hat{j}+\hat{k}, \bar{b}=4 \hat{i}-2 \hat{j}+3 \hat{k}, \bar{c}=\hat{i}-2 \hat{j}+\hat{k}\), then \(a\) vector of magnitude 6 units, which is parallel to the vector \(2 \bar{a}-\bar{b}+3 c\), isMHT CET 2024 Easy
- If \(y=x \tan y\), then \(\frac{d y}{d x}=\)MHT CET 2021 Easy
- Heart attack is also called ___________ .MHT CET 2018 Easy
- \(\int_{-5}^{5}\left[\frac{e^{x}+e^{-x}}{e^{x}-e^{-x}}\right] d x=\)MHT CET 2020 Easy
- Which of the following is NOT obtained when a mixture of methyl chloride and n-propyl chloride is treated with sodium metal in dry ether?MHT CET 2023 Easy
- For the elementary reaction, identify the correct relation among the following relations:MHT CET 2019 Easy