WELCOME By “MATHEMATICAL FORMULATION” Smt. N. Prabhavathi III Year VII(B) Elective: Linear Programming “MATHEMATICAL FORMULATION” By Smt. N. Prabhavathi Lecturer in Mathematics D.K. Govt. college for women(A) Nellore. Ph : 9440857200

LPP consists of three components namely, Linear programming is technique of making decisions under the conditions of certainty that is all objectives and constraints are quantified. LPP determines an optimum schedule of interdependent activities in view of available resources. LPP consists of three components namely, Decision variables (Activities) The objective (Goal) The constraints (restrictions)

Algorithm : Study the given situation and find the key decisions to be made. Identify the variables involved and designate them by symbols State the feasible alternatives. Identify the constraints in the problem and express them as linear inequalities. Identify the objective function and express it as a linear function of the decision variables. Each decision variable is non- negative restricted.

PROBLEM : Alpha limited produces and sells two different products under the brand names black and white. The profit per unit on these products is Rs.50 and Rs. 40 respectively. Both the products employ the same manufacturing process which has a fixed total capacity of 50,000 man hours. As per the estimates of the marketing research department of limited there is a market demand for maximum 8000 units of black and 10,000 units of white . subject to overall demand , the products can be sold in any possible combination. If it takes 3hours to produce one unit of black and 2hours to produce one unit of white , formulate the model of linear programming .

Objective function would be : Maximize Z = 50x + 40y Subject to constraints 3x +2y ≤ 50,000 x ≤ 8,000 y ≤ 10,000 And x ,y ≥ 0

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