Linear Programming Questions with Solutions

Linear programming (LPP) is a method for finding the best outcome, such as maximum profit or minimum cost, subject to a set of linear constraints. A linear programming problem has an objective function to maximise or minimise, decision variables, and constraints written as linear inequalities, along with the condition that the variables are non-negative. In MHT CET, problems are solved graphically. Draw each constraint as a line, shade the region that satisfies all the inequalities (the feasible region), and find its corner points. The optimal value of the objective function always occurs at one of these corner points, so evaluate the objective function at each one and choose the largest or smallest value. Questions also ask you to form the LPP from a word problem, identify the feasible region from a graph, or recognise when a problem has no feasible solution or an unbounded one. Practise the linear programming questions below, each with a step-by-step graphical solution.