Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
99 Percentile Qs Bank for JEE MainMathematicsStraight Lines

The maximum value of z = 6x +8y subject to x - y ≥ 0 , x + 3 y ≤ 12 , x ≥ 0 , y ≥ 0 is…..

Options

  1. A72
  2. B42
  3. C96
  4. D24

Correct answer

A. 72

Step-by-step solution

We have, z = 6x +8y Subject to constraints x - y ≥ 0 , x + 3 y ≤ 12 , x ≥ 0 , y ≥ 0 . On taking given constraints as equations, we get the following graph Intersecting point of the line x - y = 0 and x + 3 y = 12 is B (3, 3). Here, OABO is the required feasible region Whose corner points are O (0, 0), A (12, 0) and B (0, 4) Now, Corner points Z = 6 x + 8 y O (0, 0) 6 × 0 + 8 × 0 = 0 A (12, 0) 6 × 12 + 8 × 0 = 72 (maximum) B (3, 3) 6 × 3 + 8 × 3 = 42 ∴ Maximum value of Z is 72.

Practice Straight Lines on Quantrex Academy →

More from Straight Lines

If a straight line drawn through the point of intersection of the lines 4x+3y-1=0 and 3x+4y-1=0 , meets the co-ordinate axes at the points P and Q, then the locus of the mid point 2026From the point (-1, -1) , two rays are sent making angles of 45° with the line x + y = 0 . These rays get reflected from the mirror x + 2y = 1 . If the equations of the reflected r 2026In an equilateral triangle PQR , let the vertex P be at (3, 5) and the side QR be along the line x + y = 4 . If the orthocentre of the triangle PQR is ( , ) , then 9( + ) is equal 2026Let P(3 , 2 ) , 0 , be a point on the ellipse x^2 9 + y^2 4 =1 , Q be a point on the circle x^2+y^2-14x-14y+82=0 and R be a point on the line x+y=5 such that the centroid of the tr 2026Let A,B be points on the two half-lines x- 3 |y|= , >0 at a distance of from their point of intersection P . The line segment AB meets the angle bisector of the given half-lines at 2026Let the line L₁ : x + 3 = 0 intersect the lines L₂ : x - y = 0 and L₃ : 3x + y = 0 at the points A and B , respectively. Let the bisector of the obtuse angle between the lines L₂ a 2026Let the vertex A of a triangle ABC be (1, 2) , and the mid-point of the side AB be (5, -1) . If the centroid of this triangle is (3, 4) and its circumcenter is ( , ) , then 21( + ) 2026Let the mid points of the sides of a triangle ABC be ( 5 2 , 7 ) , ( 5 2 , 3 ) and (4, 5) . If its incentre is (h, k) , then 3h + k is equal to : 2026 Full Straight Lines list All 99 Percentile Qs Bank for JEE Main PYQs