We have also been given an upper bound for these variables, owing to the limitations on production by the company. However, a lower bound for the company to sell calculators is already supplied in the problem. We can note it down as: Step 2: The constraints: Since the company can’t produce a negative number of calculators in a day, a natural constraint would be: Therefore, we have 2 decision variables in this problem, namely ‘ x’ and ‘ y’. Y = number of handheld calculators produced X = number of scientific calculators produced Step 1: The decision variables: Since the question has asked for an optimum number of calculators, that’s what our decision variables in this problem would be. Hence, let us approach it in a step by step manner as discussed above. Such word problems can be very tricky to solve if not formulated properly. If each scientific calculator sold, results in a 20 rupees loss, but each handheld calculator produces a 50 rupees profit then how many of each type should be manufactured daily to maximize the net profit? Answer To satisfy a shipping contract, a minimum of 250 calculators must be shipped each day. Because of limitations on production capacity, no more than 250 scientific and 200 handheld calculators can be made daily. Long-term projections indicate an expected demand of at least 150 scientific and 100 handheld calculators each day. Question 1: A calculator company produces a handheld calculator and a scientific calculator. Now let us look at an example aimed at enabling you to learn how to formulate a problem in Linear Programming!ĭownload Linear Programming Problem Cheat Sheet Step 4: Optimize the objective function either graphically or mathematically.

Step 3: Express the objective function in the form of a linear equation in the decision variables.

all of them must be positive since the problem might represent a physical scenario, and such variables can’t be negative. Don’t forget to impose the condition of non-negativity on the decision variables i.e. This will set up our region in the n- dimensional space within which the objective function needs to be optimized. Step 2: Identify the set of constraints on the decision variables and express them in the form of linear equations / inequations.Step 1: Identify the ‘n’ number of decision variables which govern the behaviour of the objective function (which needs to be optimized).Steps towards formulating a Linear Programming problem: It usually requires a thorough understanding of the problem. Formulation of an LPP refers to translating the real-world problem into the form of mathematical equations which could be solved.

Linear programming examples in business