Step 1: Define constraints in linear programming
Constraints are the conditions or restrictions imposed on decision variables (e.g., \( x, y \)) in a linear programming problem.
They typically represent limitations on resources or other requirements.
Step 2: Identify from options
(A) Feasible solutions: These are solutions satisfying all constraints, but they are not the constraints themselves.
(B) Constraints: These are restrictions on decision variables, and this is the correct answer.
(C) Optimal solutions: These maximize or minimize the objective function but are not constraints.
(D) Infeasible solutions: These do not satisfy all constraints.
Step 3: Conclude the result
The restrictions are called constraints.
For a Linear Programming Problem, find min \( Z = 5x + 3y \) (where \( Z \) is the objective function) for the feasible region shaded in the given figure. 
In a Linear Programming Problem (LPP), the objective function $Z = 2x + 5y$ is to be maximized under the following constraints: 
\[ x + y \leq 4, \quad 3x + 3y \geq 18, \quad x, y \geq 0. \] Study the graph and select the correct option.
A racing track is built around an elliptical ground whose equation is given by \[ 9x^2 + 16y^2 = 144 \] The width of the track is \(3\) m as shown. Based on the given information answer the following: 
(i) Express \(y\) as a function of \(x\) from the given equation of ellipse.
(ii) Integrate the function obtained in (i) with respect to \(x\).
(iii)(a) Find the area of the region enclosed within the elliptical ground excluding the track using integration.
OR
(iii)(b) Write the coordinates of the points \(P\) and \(Q\) where the outer edge of the track cuts \(x\)-axis and \(y\)-axis in first quadrant and find the area of triangle formed by points \(P,O,Q\).