If `x ge 0` then show that `x ge sinx`.

If x gt a ge e , then show that, a^(x) gt x^(a) .

If |x| ge y then either x ge y or -

Given the LPP max Z=2x+3y Subject to the constraints 3x+y le3 x ge 0, y ge 0 show that the corner points of the LPP are (0,0) ,(1,0) and (0,3)

Show that m_4 ge m_2^2 .

If x, y, z are integers such that x ge 0, y ge 1, z ge 2 and x + y + z = 15, then the number of ordered triplets of the from (x,y,z) is

Make a graphical representation of the set of constraints in the following LPP Maximimize Z= x+y Subject to the constraints 5x+10y le50 x+y ge1 and x ge 0, y ge 0 show that the LPP has unique optimal solution

If z=x+iy , show that sqrt(2)|z| ge |x|+ |y| .

Solving graphically show that the following LPP has an infinite number of optimal solution Minimize Z= x+y 5x+9y le 45 x+yge2 xle 4 and x ge 0, y ge 0 Find also the minimum value of the object function Z

Given the LPP Max Z= 2x+3y Subject to the constraints 3x-y le -3 x-2y ge2 and xge 0,y ge 0 Graphically show that the LPP has no feasible solution

If x ge0 and yge0 , then the area bounded by the graph of [x] + [y] = 2 is (where [.] denotes greatest integer function)