Linear programming is a method for finding the optimal values (maximum or minimum) of quantities subject to the constraints when relationship is expressed as linear equations or inequations.
Based on the above information, answer the following questions.
(i) The optimal value of the objective function is attained at the points

(ii) The graph of the inequality 3x + 4y < 12 is

(iii) The feasible region for an LPP is shown in the figure. Let Z = 2x + 5y be the objective function. Maximum of Z occurs at

(iv) The corner points of the feasible region determined by the system of linear constraints are (0, 10), (5, 5), (15, 15), (0, 20). Let Z = px + qy, where p, q > 0. Condition on p and q so that the maximum of Z occurs at both the points (15, 15) and (0, 20) is

(v)  The corner points of the feasible region determined by the system of linear constraints are (0, 0), (0, 40), (20,40), (60,20), (60, 0). The objective function is Z = 4x + 3y. Compare the quantity in Column A and Column B

Deepa rides her car at 25 km/hr, She has to spend Rs. 2 per km on diesel and if she rides it at a faster speed of 40 km/hr, the diesel cost increases to Rs. 5 per km. She has Rs. 100 to spend on diesel. Let she travels x kms with speed 25 km/hr and y kms with speed 40 km/hr. The feasible region for the LPP is shown below:
Based on the above information, answer the following questions

Based on the above information, answer the following questions.
(i) What is the point of intersection of line l₁ and l₂,

(ii) The corner points of the feasible region shown in above graph are

(iii) If Z = x + y be the objective function and max Z = 30. The maximum value occurs at point

(iv) If Z = 6x - 9y be the objective function, then maximum value of Z is

(v) If Z = 6x + 3y be the objective function, then what is the minimum value of Z?

Corner points of the feasible region for an LPP are (0, 3), (5, 0), (6, 8), (0, 8). Let Z = 4x - 6y be the objective function.
Based on the above information, answer the following questions.
(i) The minimum value of Z occurs at

(ii) Maximum value of Z occurs at

(iii) Maximum of Z - Minimumof Z =

(iv) The corner points of the feasible region determined by the system of linear inequalities are

(v) The feasible solution of LPP belongs to

Suppose a dealer in rural area wishes to purpose a number of sewing machines. He has only Rs. 5760 to invest and has space for at most 20 items for storage. An electronic sewing machine costs him Rs. 360 and a manually operated sewing machine Rs. 240. He can sell an electronic sewing machine at a profit of Rs. 22 and a manually operated sewing machine at a profit of Rs. 18.
Based on the above information, answer the following questions.

(i) Let x and y denotes the number of electronic sewing machines and manually operated sewing machines purchased by the dealer. If it is assume that the dealer purchased atleast one of the given machines, then

(ii) Let the constraints in the given problem is represented by the following inequalities
x + y ≤ 20
360x + 240y ≤ 5760
x, y ≥ 0
Then which of the following point lie in its feasible region.

(iii) If the objective function of the given problem is maximise z = 22x + 18y, then its optimal value occur at

(iv) Suppose the following shaded region APDO, represent the feasible region corresponding to mathematical formulation. of given problem. Then which of the following represent the coordinates of one of its corner points.

(v) If an LPP admits optimal solution at two consecutive vertices of a feasible region, then

Let R be the feasible region (convex polygon) for a linear programming problem and let Z = ax + by be the objective function. When Z has an optimal value (maximum or minimum), 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.
Based on the above information, answer the following questions.
(i) Objective function of a L.P.P. is

(ii) Which of the following statement is correct?

(iii) In solving the LPP : "minimize f = 6x + 10y subject to constraints x ≥  6, Y ≥ 2, 2x + y  ≥ 10,x  ≥ 0,y ≥ 0" redundant constraints are

(iv) The feasible region for a LPP is shown shaded in the figure. Let Z = 3x - 4y be the objective function. Minimum of Z occurs at

(v) The feasible region for a LPP is shown shaded in the figure. Let F = 3x - 4y be the objective function. Maximum value of F is