Maximise Z = 3x + 4y
Subject to the constraints:x + y ≤ 4, x ≥ 0, y ≥ 0
The feasible region determined by the constraints, x + y ≤ 4, x ≥ 0, y ≥ 0, is as follows.
The corner points of the feasible region are O (0, 0), A (4, 0), and B (0, 4). The values of Z at these points are as follows.
Corner point 
Z = 3x + 4y 

O(0, 0) 
0 

A(4, 0) 
12 

B(0, 4) 
16 
→ Maximum 
Therefore, the maximum value of Z is 16 at the point B (0, 4).
In each of the following cases, state whether the function is oneone, onto or bijective. Justify your answer.
(i) f : R → R defined by f(x) = 3 – 4x
(ii) f : R → R defined by f(x) = 1 + x^{2 }
Show that the Modulus Function f : R → R, given by f(x) = x, is neither oneone nor onto, where  x  is x, if x is positive or 0 and x is – x, if x is negative.
Prove that the Greatest Integer Function f : R → R, given by f(x) = [x], is neither oneone nor onto, where [x] denotes the greatest integer less than or equal to x.
In each of the following cases, state whether the function is oneone, onto or bijective. Justify your answer.
(i) f : R → R defined by f(x) = 3 – 4x
(ii) f : R → R defined by f(x) = 1 + x^{2 }
Find the direction cosines of a line which makes equal angles with the coordinate axes.
Show that the Modulus Function f : R → R, given by f(x) = x, is neither oneone nor onto, where  x  is x, if x is positive or 0 and x is – x, if x is negative.
The radius of a circle is increasing uniformly at the rate of 3 cm/s. Find the rate at which the area of the circle is increasing when the radius is 10 cm.
Show that the Signum Function f : R → R, given by
is neither oneone nor onto.
Thanku sir