KCET · Maths · Linear Programming
The shaded region in the figure is the solution set of the inequations
- A \( 4 x+5 y \geq 20,3 x+10 y \leq 30, x \geq 6, x, y \geq 0 \)
- B \( 4 x+5 y \leq 20,3 x+10 y \leq 30, x \geq 6, x, y \geq 0 \)
- C \( 4 x+5 y \geq 20,3 x+10 y \leq 30, x \leq 6, x, y \geq 0 \)
- D \( 4 x+5 y \leq 20,3 x+10 y \leq 30, x \leq 6, x, y \geq 0 \)
Answer & Solution
Correct Answer
(C) \( 4 x+5 y \geq 20,3 x+10 y \leq 30, x \leq 6, x, y \geq 0 \)
Step-by-step Solution
Detailed explanation
Equation of line \(A B: \frac{x}{5}+\frac{y}{4}=1 \Rightarrow 4 x+5 y=20\)
Equation of line CD: \(\frac{\mathrm{x}}{10}+\frac{\mathrm{y}}{3}=1 \Rightarrow 3 \mathrm{x}+10 \mathrm{y}=30\)
Equation of line \(\mathrm{EF}: \mathrm{x}=6\)
Here we can see the shaded area above the line \(A B\), Below the line \(C D\) and Left of line EF
\(\therefore 4 x+5 y \geq 20,3 x+10 y \leq 30, x \leq 6, x, y \geq 0\)
Equation of line CD: \(\frac{\mathrm{x}}{10}+\frac{\mathrm{y}}{3}=1 \Rightarrow 3 \mathrm{x}+10 \mathrm{y}=30\)
Equation of line \(\mathrm{EF}: \mathrm{x}=6\)
Here we can see the shaded area above the line \(A B\), Below the line \(C D\) and Left of line EF
\(\therefore 4 x+5 y \geq 20,3 x+10 y \leq 30, x \leq 6, x, y \geq 0\)
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
- A bag contains \( 17 \) tickets numbered from \( 1 \) to \( 17 \). A ticket is drawn at random, then another
ticket isdrawn without replacing the first one. The probability that both the tickets may show
even numbers isKCET 2018 Easy - \( \int \frac{2 x-1}{(x-1)(x+2)(x-3)} d x=A \log |x-1|+B \log |x+2|+C \log |x-3|+K \), then \( A, B \),
C are respectivelyKCET 2019 Hard - If \(\int \frac{3 x+1}{(x-1)(x-2)(x-3)} d x A \log |x-1| B\) \(\log |x-2|+C \log |x-3|+C\), then the values of \(A, B\) and \(C\) are respectivelyKCET 2020 Medium
- \( \int \frac{1}{x^{2}\left(x^{4}+1\right)^{3 / 4}} \mathrm{dx} \) is equal toKCET 2015 Medium
- The value of \( [\vec{a}-\vec{b} \quad \vec{b}-\vec{c} \quad \vec{c}-\vec{a}] \) is equal toKCET 2014 Medium
- If \(A=\{a, b, c\}\), then the number of binary operations on \(A\) isKCET 2020 Easy
More PYQs from KCET
- Sarcomere is the functional unit of contraction in a muscle fibre. Identify the portion of myofibril that constitute a sarcomere.KCET 2016 Medium
- If \(A\) and \(B\) are two events such that \(P(A)=\frac{1}{3}, P(B)=\frac{1}{2}\) and \(P(A \cap B)=\frac{1}{6}\), then \(P\left(A^{\prime} / B\right)\) isKCET 2020 Easy
- The perimeter of a certain sector of a circle is equal to the length of the arc of the semicircle. Then, the angle at the centre of the sector in radians isKCET 2008 Easy
- If the parabola \(x^{2}=4 a y\) passes through the point \((2,1)\), then the length of the latus rectum isKCET 2020 Easy
- Which one of the following salts on being dissolved in water gives \(\mathrm{pH}>7\) at \(25^{\circ} \mathrm{C}\) ?KCET 2007 Medium
- Light of two different frequencies whose photons have energies \( 1 \mathrm{eV} \) and \( 2.5 \mathrm{eV} \) respectively,
successively illuminate a metallic surface whose work function is \( 0.5 \mathrm{eV} \). Ratio of maximum
speeds of emitted electrons will beKCET 2015 Easy