MHT CET · Maths · Linear Programming
The shaded area in the given figure is a solution set for some system of inequalities. The maximum value of the function \(z=4 x+3 y\) subject to linear constraints given by the system is
- A 38
- B 36
- C 33
- D 34
Answer & Solution
Correct Answer
(C) 33
Step-by-step Solution
Detailed explanation
The corner points of the feasible region are \(\mathrm{O}(0,0), \mathrm{A}(6,0), \mathrm{B}(6,4), \mathrm{C}(3,7)\) and \(\mathrm{D}(0,5)\).
\(z=4 x+3 y\)
At \(\mathrm{O}(0,0), \mathrm{z}=4(0)+3(0)=0\)
At \(A(6,0), z=4(6)+3(0)=24\)
At \(B(6,4), z=4(6)+3(4)=36\)
At \(C(3,7), z=4(3)+3(7)=33\)
At \(D(0,5), z=4(0)+3(5)=15\)
\(\therefore \quad\) Maximum value of z 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
- If statement I: If a quadrilateral \(A B C D\) is a square, then all of its sides are equal.
Statement II: All the sides of a quadrilateral \(A B C D\) are equal, then \(A B C D\) is a square.
ThenMHT CET 2022 Easy - If \(\mathrm{f}(x)=x^3+\mathrm{b} x^2+\mathrm{c} x+\mathrm{d}\) and \(0 < \mathrm{b}^2 < \mathrm{c}\), then in \((-\infty, \infty)\)MHT CET 2023 Easy
- The objective function , subject to has maximum value _________ of the feasible region.MHT CET 2016 Hard
- A right circular cone has height \(9 \mathrm{~cm}\) and radius of base \(5 \mathrm{~cm}\). It is inverted and water is poured into it. If at any instant, the water level rises at the rate \(\frac{\pi}{\mathrm{A}} \mathrm{cm} / \mathrm{sec}\). where \(\mathrm{A}\) is area of the water surface at that instant, then cone is completely filled inMHT CET 2023 Medium
- If \((p \wedge \sim r) \rightarrow(\sim p \vee q)\) has truth value False, then truth values of \(p, q, r\) are respectively.MHT CET 2024 Easy
- Let
\(\mathrm{f}(\mathrm{x}) \begin{cases}=\mathrm{x}+\mathrm{a} \sqrt{2} \sin \mathrm{x}, & 0 \leq \mathrm{x} < \frac{\pi}{4} \ =2 \mathrm{x} \cot \mathrm{x}+\mathrm{b}, \end{cases}\) \(\frac{\pi}{4} \leq \mathrm{x} < \frac{\pi}{2} \) \(=\mathrm{a} \cos 2 \mathrm{x}-\mathrm{b} \sin \mathrm{x}, \frac{\pi}{2} \leq \mathrm{x} \leq \pi\) If \(\mathrm{f}(\mathrm{x})\) is continuous for \(0 \leq \mathrm{x} \leq \pi\), thenMHT CET 2021 Hard
More PYQs from MHT CET
- Let \(\bar{a}=\hat{i}+\hat{\mathrm{j}}+\hat{\mathrm{k}}, \overline{\mathrm{b}}\) and \(\overline{\mathrm{c}}=\hat{\mathrm{j}}-\hat{\mathrm{k}}\) be three vectors such that \(\bar{a} \times \overline{\mathrm{b}}=\overline{\mathrm{c}}\) and \(\bar{a} \cdot \bar{c}=0\). If the length of projection vector of the vector \(\overline{\mathrm{b}}\) on the vector \(\bar{a} \times \overline{\mathrm{c}}\) is \(l\), then the value of \(3 l^2\) isMHT CET 2025 Hard
- Butylated hydroxyl anisole isMHT CET 2016 Easy
- An e.m.f. \(E=E_0 \cos \omega t\) is applied to circuit containing \(L\) and \(R\) in series. If \(X_L=2 R\), then the power dissipated in the circuit isMHT CET 2024 Medium
- Identify a formula of coordinates complex Bis(ethylenediamine) dithiocyanatoplatinum (IV).MHT CET 2022 Easy
- Match the pair.
Column I
(Disorder / disease)Column II
(Symptoms)Q.1. Nephritis a. oligouria Q.2. Chronic kidney disease b. proteinuria Q.3. Acute renal failure с. reduced kidney size Q.4. Kidney stones d. hazy urine
Choose the correct answer from the following options.MHT CET 2025 Hard - A progressive wave is given by, \(Y=12 \sin (5 t-4 x)\). On this wave, how far away are the two points having a phase difference of \(90^{\circ}\) ?MHT CET 2023 Medium