MHT CET · Maths · Linear Programming
If \(\mathrm{Z}=7 x+y\) subject to \(5 x+y \geq 5, x+y \geq 3, x \geq 0, y \geq 0\), then minimum
value of \(\mathrm{Z}\) is
- A 2
- B 5
- C 6
- D 3
Answer & Solution
Correct Answer
(B) 5
Step-by-step Solution
Detailed explanation
Feasible area is shaded.
Point of intersection of given lines is \(\mathrm{P} \equiv\left(\frac{1}{2}, \frac{5}{2}\right)\)
Co-ordinates of points are as follows :
\(C \equiv(3,0) ; P \equiv\left(\frac{1}{2}, \frac{5}{2}\right)\) and \(B \equiv(0,5)\)
We have \(Z=7 x+y\)
\(Z_{(c)}=21+0=21\)
\(\therefore \quad Z_{(B)}=0+5=5\)
\(Z_{(P)}=\frac{7}{2}+\frac{5}{2}=6\)
Thus minimum value is 5.
Point of intersection of given lines is \(\mathrm{P} \equiv\left(\frac{1}{2}, \frac{5}{2}\right)\)
Co-ordinates of points are as follows :
\(C \equiv(3,0) ; P \equiv\left(\frac{1}{2}, \frac{5}{2}\right)\) and \(B \equiv(0,5)\)
We have \(Z=7 x+y\)
\(Z_{(c)}=21+0=21\)
\(\therefore \quad Z_{(B)}=0+5=5\)
\(Z_{(P)}=\frac{7}{2}+\frac{5}{2}=6\)
Thus minimum value is 5.
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 the function is continuous at x = 0, then k = ….MHT CET 2019 Medium
- If \(\mathrm{A}\left[\begin{array}{cc}5 \mathrm{a} & -\mathrm{b} \\ 3 & 2\end{array}\right]\) and \(\mathrm{A}\) adj \(\mathrm{A}=\mathrm{AA}^{\mathrm{T}}\), then \(5 \mathrm{a}+\mathrm{b}=\)MHT CET 2021 Medium
- IfMHT CET 2016 Medium
- If the volume of the parallelopiped is \(158 \mathrm{cu}\). units whose coterminus edges are given by the vectors \(\bar{a}=(\hat{i}+\hat{j}+n \hat{k}), \bar{b}=2 \hat{i}+4 \hat{j}-n \hat{k}\) and \(\bar{c}=\hat{i}+n \hat{j}+3 \hat{k}\), where \(n \geq 0\), then the value of \(n\) isMHT CET 2023 Medium
- If \(\overline{\mathrm{a}}, \overline{\mathrm{b}}, \overline{\mathrm{c}}\) are mutually perpendicular vectors having magnitudes \(1,2,3\) respectively, then the value of \(\left[\begin{array}{lll}\bar{a}+\bar{b}+\bar{c} & \bar{b}-\bar{a} & \bar{c}\end{array}\right]\) isMHT CET 2024 Medium
- If \(y=\log \tan \left(\frac{x}{2}\right)+\sin ^1(\cos x)\), then \(\frac{d y}{d x}=\)MHT CET 2021 Medium
More PYQs from MHT CET
- Let X be a discrete random variable. The probability distribution of X is given below
\(\begin{array}{|l|c|c|c|} \hline \mathrm{X} & 30 & 10 & -10 \\ \hline \mathrm{P}(\mathrm{X}) & \frac{1}{5} & \mathrm{~A} & \mathrm{~B} \\ \hline \end{array}\)
and \(\mathrm{E}(\mathrm{X})=4\), then the value of AB is equal toMHT CET 2025 Medium - The area of the region bounded by the curve \(y^2=4 x\) and the line \(y=x\) isMHT CET 2021 Easy
- \(\int(1+x) \log x \mathrm{~d} x=\)MHT CET 2020 Medium
- What is the heat of formation of \(\mathrm{HCl}_{(\mathrm{g})}\) from following equation? \(\mathrm{H}_{2(\mathrm{~g})}+\mathrm{Cl}_{2(\mathrm{~g})} \rightarrow 2 \mathrm{HCl}_{(\mathrm{g})} \Delta_{\mathrm{f}} \mathrm{H}=-194 \mathrm{~kJ}\)MHT CET 2022 Easy
- If \(A=2 \tan ^{-1}\left(\frac{1+x}{1-x}\right)\) and \(B=\cos ^{-1}\left(\frac{1-x^2}{1+x^2}\right)\), where \(x \in(0,1)\), then \(A-B=\)MHT CET 2022 Hard
- What is IUPAC name of the following compound?
MHT CET 2024 Easy