Numericals on Formulation Method of Linear Programming

(Formulation)

1.         Raja Furniture factory produces inexpensive tables and chairs. Production process on both are similar in the sense that both require a certain number of carpentry work and a certain number of labour hours in the painting department. Each table takes 4 hours in carpentry and 2 hours in painting department. Each chair needs 3 hours in carpentry shop and just one hour in painting. During the current production period, only 300 hours of carpentry time and 120 hours of painting time are available. Each table sold yields a profit of ` 70 and each chair produced may be sold for a profit of ` 50.

Raja furniture factory wants to determine the best possible combination of tables & chairs to manufacture in order to get maximum profit. Assuming that any mix of table and chairs could be sold, the manufacturer would like this production mix situation to be formulated as a linear programming problem.

                                                                           (Ans :  Maximize (total profit) Z = 70x₁ + 50x₂

Subject to                    4x₁ + 3x₂ \<300

2x₁ + x₂  \<120

x_1, x₂  >/0)

2.        A dietician in an institution has to decide the food mix for the inmates. The dietary requirements are that each inmate must get at least :

Two gms each of protein and fat and 4 gms of carbohydrates.

But the carbohydrate should not exceed 6 gms per person.

The availability of protein, fat and carbohydrate in gms. Per kg of foods A, B and C is given as follows :

Formulate the problem as LPP. So as to obtain the diet per person per day at minimum cost.

(Ans :  Minimize C = 30x₁ + 50x₂ + 4x₃

Subject to 10x₁ + 2x₂ + 2x_{3 >/} 2

2x₁ + x₂ >/ 2

15x₂ + 10x_{3 >/} 4

15x₂ + 10x_{3 \<}6

x_1, x_2, x₃  >/0)