Linear Programming

Mathematical Formulation of Linear programing problem(Example)

If a young man rides his motorcycle at 25 km/hr, he has to spend 2 per kilometer on petrol if per he rides it at a faster speed of 40 km/hr the petrol cost increases to 5 per kilometer.He has 100 to spend on petrol and wishes to find the maximum distance he can travel within one hours. Express this as a linear programming problem and then solve it.

If a young man drives his car at 40 km per hour, he has to spend ₹ 5 per km on petrol, if he drives it at a slower speed of 25 km per hour, the petrol cost decreases to ₹ 2 per km. He has ₹ 100 to spend on petrol and wishes to find thhe maximum distance he can travel within one hour.Express this as a linear programming problem and then solve it.

Food F_1 contains 5 units of vitamin A and 6 units of vitamin B per gram and costs 20 p/gm. Food F_2 contains 8 units of vitamin A and 10 units of vitamin B per gram and costs 30 p/gm. The daily requirements of A and B are at least 80 and 100 units respectively. Formulate the problem as a linear programming problem to minimize cost.

A dealer deals in two items A and B He has Rs. 15000 to invest and a space to store almost 80 pieces Item A costs him Rs 300 and item B costs him Rs. 150 He can sell items A and B at profits of Rs 40 and Rs 25 respectively Assuming that he can sell all that he buys formulate the above as a linear programming prioblem for maximum profit and solve it graphically

A factory uses three different resources for the manufacture of two different productoof the resource A, 12 units of B and 16 unit of C being available. One unit of there quires 2, 2 and 4 units of the respective resources and one unit of the second requires 4,2 and 0 units of respective resources. It is known that the first product givesatof 2 monetary units per unit and the second 3. Formulate the linear programming problem How many units of each product should be manufactured for maximizing the profit? solve it graphically.

Let R be the feasible region (convex polygon) for a linear programming problem and Z = ax + by be the objective function. Then, which of the following statements is false? A) When Z has an optimal value, where the variables x and y are subject to constraints described by linear inequalities, this optimal value must occur at a corner point (vertex) of the feasible region . B)If R is bounded, then the objective function Z has both a maximum and a minimum value on Rand each of these occurs at a corner point of R . C) If R is unbounded, then a maximum or a minimum value of the objective function may not exist D) If R is unbounded and a maximum or a minimum value of the objective function z exists, it must occur at corner point of R

Draw the graph of the following linear programing as 50x+25y =0,y>=0 are constraints.