Linear Programming

Maths · Class 12

Simulation · Maths · Class 12

Hunt for the most profitable plan

"Hunt for the most profitable plan" is a free, interactive Class 12 Maths simulation for JEE, built on the lesson "The corner point method" in Linear Programming. X is the number of cupcake trays and y the number of cookie trays. The shaded region holds every plan the oven (2x + y ≤ 24) and the flour (x + y ≤ 16) allow. Move the plan around and watch the profit Z = 150x + 100y. Inside the region there is always a better plan nearby; the profit is largest at a corner. Checking O, A(12, 0), B(8, 8), C(0, 16) gives 0, 1800, 2000 and 1600, so B wins.

From the lesson The corner point method in Linear Programming. Change the values and watch what happens.

Hunt for the most profitable planMaths · Class 12

The idea behind it

NCERT §12.2.2, Examples 1–2

  • Step 1: draw the feasible region and find all its corners, by inspection or by solving the two boundary equations that meet at each.
  • Step 2: evaluate Z at every corner. Call the largest value M and the smallest m.
  • Step 3: if the region is bounded, M is the maximum and m the minimum of Z.
  • Dealer: Z = 250x + 75y is 0 at O, 5000 at A(20, 0), 6250 at B(10, 50) and 4500 at C(0, 60). The maximum profit Rs 6250 comes from buying 10 tables and 50 chairs.
  • B is where 5x + y = 100 meets x + y = 60: subtracting gives 4x = 40, so x = 10 and y = 50.
  • Maximise Z = 4x + y with x + y ≤ 50, 3x + y ≤ 90, x, y ≥ 0: the corners (0, 0), (30, 0), (20, 30), (0, 50) give 0, 120, 110, 50, so the maximum is 120 at (30, 0).
  • Minimise Z = 200x + 500y with x + 2y ≥ 10, 3x + 4y ≤ 24, x, y ≥ 0: the region is the triangle (0, 5), (4, 3), (0, 6), with Z = 2500, 2300, 3000, so the minimum is 2300 at (4, 3).
  • Minimising uses exactly the same table; only the choice of the smallest entry changes.

Questions

2 answers

What does the "Hunt for the most profitable plan" simulation show?
X is the number of cupcake trays and y the number of cookie trays. The shaded region holds every plan the oven (2x + y ≤ 24) and the flour (x + y ≤ 16) allow. Move the plan around and watch the profit Z = 150x + 100y.
Is this simulation free?
Yes. It is free and runs in the browser on a phone or a laptop. It belongs to the lesson "The corner point method" in Linear Programming (Class 12 Maths).

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