Linear programming
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Linear programming is a technique to allocate limited resources to optimize an objective like profit maximization. It involves identifying decision variables, constraints, and the objective function. An example problem maximizes profit from manufacturing dolls and guns given constraints on machine hours and profit per item. The objective is to maximize profit which is formulated as a linear function of doll and gun units, subject to constraints on machine hours from each item.
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- 3. Formulation of LPP:- To identify the decision variables. To identify all the limitations. To identify the objective to be optimized (maximization or minimization).
- 4. Example 1:- A toy manufacturer produces 2 types of toys, dolls and guns, each of which must be processed through 2 machines A and B. The maximum availability of machines A and B per day are 18 and 10 hours respectively. Manufacturing a doll requires 2 hours in machine A and B both but manufacturing a gun requires 3 hours in machine A and 1 hour in machine B. If the profit per doll is 9 Rs and per gun is 13 Rs, formulate the problem to maximize the profit.
- 5. Maximize Z = 9x+ 13y(Objective function) Subject to the conditions:- 2x+3y£18 2x+y£10constraints x³ 0, y³0