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Inequalities and linear programming
Class 12 · Mathematics · 7 questions
Name: ____________________ Date: ____________
In linear programming, the region satisfying all the constraints is called the:
- A Feasible region
- B Objective
- C Boundary only
- D Optimal point
The optimal value of a linear objective function over a feasible region occurs at a:
- A Origin always
- B Corner point
- C Outside the region
- D Midpoint
The inequality 2x + y less than or equal to 6 includes the point:
- A (4, 1)
- B (3, 3)
- C (5, 5)
- D (1, 1)
Maximise z = x + y subject to x + y at most 4, x and y at least 0. The maximum value is:
- A 8
- B 4
- C 2
- D 0
The inequalities x at least 0 and y at least 0 restrict the region to the:
- A Second quadrant
- B First quadrant
- C Fourth quadrant
- D Third quadrant
A constraint in a linear programming problem is a:
- A Linear inequality
- B Matrix
- C Quadratic equation
- D Constant
An unbounded feasible region means the objective can:
- A Be exactly zero only
- B Increase without limit in some direction
- C Never be positive
- D Be negative only
Answer key
1. A, 2. B, 3. D, 4. B, 5. B, 6. A, 7. B
It is the set of all points that meet the constraints.
The maximum or minimum is at a vertex.
2 + 1 = 3, which is at most 6.
The best corner points give x + y = 4.
Both coordinates are non negative.
It limits the variables.
No upper limit is set by the constraints.