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.
Solve the following linear programming problem graphically:
Maximize \( z = x + y \), subject to constraints:
\[ 2x + 5y \leq 100, \quad 8x + 5y \leq 200, \quad x \geq 0, \quad y \geq 0. \]