MHT CET · Maths · Application of Derivatives
The objective function of LPP defined over the convex set attains its optimum value at
- A At least two of the corner points
- B All the corner points
- C At least one of the corner points
- D None of the corner points
Answer & Solution
Correct Answer
(C) At least one of the corner points
Step-by-step Solution
Detailed explanation
Let \(Z=a x+\) by be the objective function
When Z has optimum value(maximum or minimum), where the variables \(x\) and \(y\) are subject to constraints described by linear inequalities, this optimum value must occur at a corner points of the feasible region.
Thus, the function attains its optimum value at one of the corner points.
When Z has optimum value(maximum or minimum), where the variables \(x\) and \(y\) are subject to constraints described by linear inequalities, this optimum value must occur at a corner points of the feasible region.
Thus, the function attains its optimum value at one of the corner points.
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
- If \(\overline{\mathrm{u}}, \overline{\mathrm{v}}\) and \(\overline{\mathrm{w}}\) are three non-coplanar vectors, then \((\bar{u}+\bar{v}-\bar{w}) \cdot[(\bar{u}-\bar{v}) \times(\bar{v}-\bar{w})]\) is equal toMHT CET 2024 Hard
- The function \(f(x)=2 x^3-9 x^2+12 x+29\) is monotonically increasing in the intervalMHT CET 2022 Easy
- Which of the following is not a homogeneous function?MHT CET 2025 Easy
- The equation of the normal to the curve \(3 x^2-y^2=8\), which is parallel to the line \(x+3 y=10\), isMHT CET 2023 Easy
- If \(\int \frac{2 x+3}{(x-1)\left(x^2+1\right)} \mathrm{d} x=\log _e\left\{(x-1)^{\frac{5}{2}}\left(x^2+1\right)^a\right\}-\frac{1}{2} \tan ^{-1} x+\mathrm{A}\) where \(A\) is an arbitrary constant, then the value of \(a\) isMHT CET 2025 Medium
- If \(x y=\tan ^{-1}(x y)+\cot ^{-1}(x y)\), then \(\frac{d y}{d x}\) is equal
toMHT CET 2009 Easy
More PYQs from MHT CET
- The potential difference \(\left(\mathrm{V}_{\mathrm{A}}-\mathrm{V}_{\mathrm{B}}\right)\) between the points ' A ' and ' B ' in the given part of the circuit is
MHT CET 2024 Easy - If
\(\int(7 x-2) \sqrt{3 x+2} \mathrm{~d} x=\mathrm{A}(3 x+2)^{\frac{5}{2}}+\mathrm{B}(3 x+2)^{\frac{3}{2}}+\mathrm{c}\)
(where c is a constant of integration), then the values of \(A\) and \(B\) are respectivelyMHT CET 2024 Easy - A beam of light of intensity \(I_0\) falls on a system of three polaroids which are arranged in succession such that the pass (transmission) axis is turned through \(60^{\circ}\) with respect to preceding one. The fraction of the incident light intensity that passes through the system is
\(\left(\cos 60^{\circ}=1 / 2\right)\)MHT CET 2025 Medium - Identify the catalyst used in the manufacture of high density polythene.MHT CET 2020 Easy
- Let be the mass and be the length of a thin uniform rod. In first case, axis of rotation is passing through center and perpendicular to the length of the rod. In second case axis of rotation is passing through one end and perpendicular to the length of the rod. The ratio of radius of gyration in first case to second case isMHT CET 2016 Easy
- Which among the following substituent groups decreases the acidic strength of aromatic carboxylic acid?MHT CET 2020 Easy