enEnglishguગુજરાતી
JEE Mains · Maths · STD 12 - 12. linear programming
The maximum value of \(z\) in the following equation \(z=6 x y+y^{2},\) where \(3 x+4 y \leq 100\) and \(4 x+3 y \leq 75\) for \(x \geq 0\) and \(y \geq 0\) is \(......\)
- A \(904\)
- B \(846\)
- C \(952\)
- D \(882\)
Answer & Solution
Correct Answer
(A) \(904\)
Step-by-step Solution
Detailed explanation
\(z=6 x y+y^{2}=y(6 x+y)\) \(3 x+4 y \leq 100\) \(....(i)\) \(4 x+3 y \leq 75\) \(......(ii)\) \(x \geq 0\) \(y \geq 0\) \(z \leq \frac{75-3 y}{4}\) \(Z=y(6 x+y)\) \(Z \leq y\left(6 \cdot\left(\frac{75-3 y}{4}\right)+y\right)\)…
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 \(\int {\frac{{dx}}{{x + {x^7}}}} = p(x)\) then, \(\int {\frac{{{x^6}}}{{x + {x^7}}}} dx\) is equal toJEE Mains 2013 Hard
- Using the principal values of the inverse trigonometric functions, the sum of the maximum and the minimum values of \(16\left(\left(\sec ^{-1} x\right)^2+\left(\operatorname{cosec}^{-1} x\right)^2\right)\) is :JEE Mains 2025 Medium
- The locus of the point of intersection of the lines, \(\sqrt 2 x - y + 4\sqrt 2 k = 0\) and \(\sqrt 2 kx + ky - 4\sqrt 2 = 0\) ( \(k\) is any non-zero real parameter) isJEE Mains 2018 Hard
- The plane, passing through the points \((0,-1,2)\) and \((-1,2,1)\) and parallel to the line passing through \((5\), \(1,-7)\) and \((1,-1,-1)\), also passes through the point.JEE Mains 2023 Hard
- Let the coefficient of \(x^{\mathrm{r}}\) in the expansion of \((\mathrm{x}+3)^{\mathrm{n}-1}+(\mathrm{x}+3)^{\mathrm{n}-2}(\mathrm{x}+2)+\) \((\mathrm{x}+3)^{\mathrm{n}-3}(\mathrm{x}+2)^2+\ldots \ldots+(\mathrm{x}+2)^{\mathrm{n}-1}\) be \(\alpha_{\mathrm{r}}\). If \(\sum_{\mathrm{r}=0}^{\mathrm{n}} \alpha_{\mathrm{r}}=\beta^{\mathrm{n}}-\gamma^{\mathrm{n}}, \beta, \gamma \in \mathrm{N}\), then the value of \(\beta^2+\gamma^2\) equals ...........JEE Mains 2024 Hard
- If \(A=\begin{bmatrix}2&3\\ 3&5\end{bmatrix}\), then the determinant of the matrix \((A^{2025}-3A^{2024}+A^{2023})\) isJEE Mains 2026 Medium
More PYQs from JEE Mains
- Let the area of the triangle formed by a straight Line L: \(\mathrm{x}+\mathrm{by}+\mathrm{c}=0\) with co-ordinate axes be 48 square units. If the perpendicular drawn from the origin to the line L makes an angle of \(45^{\circ}\) with the positive x -axis, then the value of \(\mathrm{b}^2+\mathrm{c}^2\) is:JEE Mains 2025 Easy
- If \(x^{2}+9 y^{2}-4 x+3=0, x, y \in R\), then \(x\) and \(y\) respectively lie in the intervals:JEE Mains 2021 Hard
- Let \(f(x) = \begin{cases} \dfrac{1}{3}, & x \leq \pi/2 \\ \dfrac{b(1-\sin x)}{(\pi-2x)^2}, & x > \pi/2 \end{cases}\). If \(f\) is continuous at \(x=\pi/2\), then the value of \(\displaystyle\int_{0}^{3b-6} |x^2+2x-3|\,dx\) is:JEE Mains 2026 Hard
- If \(0\, \le \,x\, < \frac{\pi }{2},\) then the number of values of \(x\) for which \(sin\,x -sin\,2x + sin\,3x=0,\) isJEE Mains 2019 Hard
- Let \(f :[-3,1] \rightarrow R\) be given as \(f(x)=\left\{\begin{array}{ll} \min \left\{(x+6), x^{2}\right\}, & -3 \leq x \leq 0 \\ \max \left\{\sqrt{x}, x^{2}\right\}, & 0 \leq x \leq 1 \end{array}\right.\) If the area bounded by \(y = f ( x )\) and \(x\) -axis is \(A,\) then the value of \(6 A\) is equal to ....... .JEE Mains 2021 Hard
- Consider an arithmetic series and a geometric series having four initial terms from the set \(\{11,8,21,16,26,32,4\}\) If the last terms of these series are the maximum possible four digit numbers, then the number of common terms in these two series is equal to .......JEE Mains 2021 Medium