Linear Programming.

9 lessons69 min2 simulations

Linear programming finds the optimal plan when a quantity to be made as large (or as small) as possible depends linearly on two unknowns, and the unknowns are held back by a handful of linear limits. The chapter turns a word problem into three pieces: decision variables x and y, the constraints as linear inequalities with x, y ≥ 0, and the objective Z = ax + by. The inequalities cut out a feasible region, and a key fact makes the problem finite: whenever Z has a best value on that region, one of the region's corner points gives it. So the whole method is to draw the region, list its corners, and compare Z at each. The chapter then looks at the cases where this needs care: two corners that tie, a region that runs off to infinity, and constraints that no point can satisfy together.

Also called: LPP · linear programming problems