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Class 12 Linear Programming worksheet
CBSE Mathematics. Feasible regions, corner points, maximising and minimising, word problems. Every sheet has 20 questions in three sections and an answer key, and the numbers change every time.
Sample questions
Real questions from this chapter, as the app sets them. Tap Answer to see the answer and working.
Section A · multiple choice
- 1.
The corner points of a feasible region are (0, 0), (3, 0), (2, 6), (0, 8). The maximum of Z = 4x + 9y is:
- 72
- 0
- 12
- 62
Answer
(a) 72
Z(0, 0) = 0, Z(3, 0) = 12, Z(2, 6) = 62, Z(0, 8) = 72
- 2.
The corner points of a bounded feasible region are (0, 12), (6, 4), (10, 0), (10, 12). The minimum of Z = 7x + 9y is:
- 178
- 108
- 78
- 70
Answer
(d) 70
Z(0, 12) = 108, Z(6, 4) = 78, Z(10, 0) = 70, Z(10, 12) = 178
- 3.
Which point lies in the feasible region of x + y ≤ 13, x + 2y ≤ 20, x ≥ 0, y ≥ 0?
- (7, 8)
- (0, 11)
- (5, 6)
- (14, 0)
Answer
(c) (5, 6)
(5, 6) satisfies every constraint
Section B · short answer
- 4.
Maximise Z = 8x + 4y subject to x + 4y ≤ 20, x + y ≤ 11, x ≥ 0, y ≥ 0.
Answer
maximum 88 at (11, 0)
corners (0, 0), (11, 0), (8, 3), (0, 5): Z(0, 0) = 0, Z(11, 0) = 88, Z(8, 3) = 76, Z(0, 5) = 20
- 5.
Minimise Z = 3x + 2y subject to x + 2y ≥ 22, x + y ≥ 14, x ≥ 0, y ≥ 0.
Answer
minimum 28 at (0, 14)
the region is unbounded; Z(0, 14) = 28, Z(6, 8) = 34, Z(22, 0) = 66; no point has 3x + 2y < 28
Section C · long answer
- 6.
A workshop makes tables and chairs. A table needs 1 hour of cutting and 4 hours of finishing; a chair needs 1 hour and 3 hours. There are 10 cutting hours and 36 finishing hours a week. The profit is Rs 10 on a table and Rs 20 on a chair. How many of each give the most profit, and what is it?
Answer
maximum profit Rs 200 at (0, 10)
Maximise Z = 10x + 20y subject to x + y ≤ 10, 4x + 3y ≤ 36, x ≥ 0, y ≥ 0; Z(0, 0) = 0, Z(9, 0) = 90, Z(6, 4) = 140, Z(0, 10) = 200
Fresh sheets for your child
In the app, every Linear Programming sheet is new: the app remembers the questions your child has already had and leaves them out. Print the sheet as a PDF, or use notebook mode and write the answers in a notebook.
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