Linear programming
Find the best value of Z at the corners of the feasible region.
Learn with Kutty
Go one screen at a time. Press Next when you are ready. Tap 🔊 Read to me to listen.
Find the best choice when you have limits. The best is always at a corner.
Look: The green area is every allowed choice. Only the 4 corners need checking.
✏️ Your turn!
Type your answer and press Check. Kutty will tell you if it is right.
1Corners (0, 0), (5, 0), (0, 4). Best of 2x + 3y?
2Is 2 cakes and 2 pies allowed?
3Is 5 cakes and 1 pie allowed?
! Careful!
✗Testing points in the middle.
✓The best is always at a corner.
✗Forgetting you cannot make negative cakes.
✓x ≥ 0 and y ≥ 0 are limits too.
See the whole lesson on one page
Find the best choice when you have limits. The best is always at a corner.
Draw each limit as a line. Shade where all limits are OK. Test the corners of that region: one of them is the best.
Think of it like thisA baker has limited flour and time. How many cakes and pies give the most profit? Check only the corner choices.
Solved together
Cakes earn ₹30, pies ₹20. Flour allows 5 items in all; time allows 2 per cake and 1 per pie, 8 hours total. What is the best plan?
Corners of the allowed area: (0, 0), (4, 0), (3, 2), (0, 5).
Work out the profit at each corner.
Answer3 cakes and 2 pies: ₹130.
Now practise it
Kanakku makes new questions on linear programming every time. It shows the working and gives a hint when you are stuck.