Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
MHT CET2019Morning ShiftMathematicsArea Under CurvesActual

If z = a x + b y ; a , b > 0 subject to x ≤ 2 , y ≤ 2 , x + y ≥ 3 , x ≥ 0 , y ≥ 0 has minimum value at 2,1 only, then…

Options

  1. Aa > b
  2. Ba = b
  3. Ca < b
  4. Da = 1 + b

Correct answer

C. a < b

Step-by-step solution

We have, z = a x + b y , a , b > 0 Subject to constraints x ≤ 2 , y ≤ 2 , x + y ≥ 3 x , y ≥ 0 On taking given constraints as equation, we get the following graph Here, ABCA is the required feasible region whose corner points are A 2,1 , B 1,2 and C 2,2 . Since, It is given that z = a x + b y ; a , b > 0 has minimum value at 2,1 ∴ Value of z at 2,1 < value of z at 1,2 ⇒ 2 a + b < a + 2 b ⇒ a < b

Practice Area Under Curves on Quantrex Academy →

More from Area Under Curves

Find the area bounded by the curve y = |2 - x| , the x –axis, and the lines x = 0 and x = 5 2026The area enclosed by the curve y = -x^2 and the line x + y + 2 = 0 is 2026The area of the region bounded by the line y = x + 2 and the curve x = -y^2 is 2026The area of the region in the first quadrant enclosed by the x -axis, the line x = 3 ,y and the circle x^2 + y^2 = 4 is 2026The area of the region bounded by the curve y^2 = x^3 , the y -axis and the lines y = 1 and y = 8 is 2026The area enclosed by the curve x = 3 , y = 3 is 2026The area in square units of the region bounded by the curve y = 16 - x^2 and lines x = 0, x = 4 above the X-axis is 2026The area bounded by the curves y = |x| - 1 and y = -|x| + 1 is 2026 Full Area Under Curves list All MHT CET PYQs