MHT CET · Maths · Linear Programming
Maximum value of \(\mathrm{Z}=100 x+70 y\) Subject to \(2 x \geq 4, y \leq 3, x+y \leq 8, x, y \geq 0\) is
- A 800 .
- B 940 .
- C 400 .
- D 710 .
Answer & Solution
Correct Answer
(A) 800 .
Step-by-step Solution
Detailed explanation
The feasible region lies on the origin side of \(y=3\) and \(x+y=8\), and on non-origin side of \(2 x=4\), in the first quadrant.
The corner points of the feasible region are \(\mathrm{A}(2,0), \mathrm{B}(8,0), \mathrm{C}(5,3)\) and \(\mathrm{D}(2,3)\).
\(\mathrm{Z}=100 x+70 y\)
At A(2, 0), Z= 200
At B( 8,0\(), Z=800\)
At C(5,3), Z= 710
At D(2, 3), Z= 410
\(\therefore \quad\) Maximum value of \(Z\) is 800 .
The corner points of the feasible region are \(\mathrm{A}(2,0), \mathrm{B}(8,0), \mathrm{C}(5,3)\) and \(\mathrm{D}(2,3)\).
\(\mathrm{Z}=100 x+70 y\)
At A(2, 0), Z= 200
At B( 8,0\(), Z=800\)
At C(5,3), Z= 710
At D(2, 3), Z= 410
\(\therefore \quad\) Maximum value of \(Z\) is 800 .
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 \(\mathrm{G}(3,-5, \mathrm{r})\) is the centroid of \(\triangle \mathrm{ABC}\), where \(\mathrm{A} \equiv(7,-8,1)\), \(B \equiv(p, q, 5), C \equiv(q+1,5 p, 0)\) are vertices of the triangle \(A B C\), then the values of \(p, q, r\) are respectivelyMHT CET 2021 Easy
- For a sequence if \(S_{n}=\frac{5^{n}-2^{n}}{2^{n}}\), then its fourth term isMHT CET 2020 Medium
- If \(1-\cos \theta=\sin \theta \cdot \sin \frac{\theta}{2}\), then the value of \(\theta\) isMHT CET 2025 Medium
- If vectors \(\bar{a}=2 \hat{i}+2 \hat{j}+3 \hat{k}, \bar{b}=-\hat{i}+2 \hat{j}+\hat{k}\) and \(\bar{c}=-3 \hat{i}+\hat{j}+2 \hat{k}\) are such that, \(\overline{\mathrm{a}}+\lambda \overline{\mathrm{b}}\) is perpendicular to \(\overline{\mathrm{c}}\), then \(\lambda=\)MHT CET 2021 Easy
- The Y-intercept of the common tangent to the parabola \(y^2=32 x\) and \(x^2=108 y\) isMHT CET 2025 Easy
- \( \sin ^{-1}\left[\sin \left(-600^{\circ}\right)\right]+\cot ^{-1}(-\sqrt{3})= \)MHT CET 2021 Medium
More PYQs from MHT CET
- A diatomic gas \(\left(\gamma=\frac{7}{5}\right)\) is compressed adiabatically to volume \(\frac{V_i}{32}\) where \(V_i\) is its initial volume. The initial temperature of the gas is \(T_i\) in Kelvin and the final temperature is '\(xT_{\mathrm{i}}\) '. The value of ' \(x\) ' isMHT CET 2023 Medium
- The growth of population is proportional to the number present. If the population of a colony doubles is 50 years, then the population will become triple in _____ yearsMHT CET 2020 Medium
- If \(\tan ^{-1}(x+1)+\tan ^{-1} x+\tan ^{-1}(x-1)=\tan ^{-1} 3\), then for \(x < 0\) the value of \(500 x^4+270 x^2+997=\)MHT CET 2025 Medium
- A black body emits radiation of maximum intensity at wavelength ' \(\lambda\) ' at temperature T K. Its corresponding wavelength at temperature \(1 \cdot 5 \mathrm{~T} \mathrm{~K}\) will beMHT CET 2025 Easy
- Two solid spheres of radii \(R_1\) and \(R_2\) made of same material and have similar surfaces. The spheres are raised to the same temperature and then allowed to cool under identical conditions. Assuming spheres to be perfect conductors of heat, then the ratio of initial rates of cooling areMHT CET 2022 Easy
- Given below are two statements.
Statement I - Most of the blood proteins are acidic proteins.
Statement II - Derived proteins are not found in nature.
In the light of above statements, Select the correct option given below:MHT CET 2025 Easy