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प्रश्न
If the constraints in a linear programming problem are changed
विकल्प
the problem is to be re-evaluated
solution is not defined
the objective function has to be modified
the change in constraints is ignored
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उत्तर
the problem is to be re-evaluated
The optimisation of the objective function of a LPP is governed by the constraints.
Therefore, if the constraints in a linear programming problem are changed, then the problem needs to be re-evaluated.
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संबंधित प्रश्न
A firm manufactures two types of products A and B and sells them at a profit of Rs 2 on type A and Rs 3 on type B. Each product is processed on two machines M1 and M2. Type A requires one minute of processing time on M1 and two minutes of M2; type B requires one minute on M1 and one minute on M2. The machine M1 is available for not more than 6 hours 40 minutes while machine M2 is available for 10 hours during any working day. Formulate the problem as a LPP.
A manufacturer can produce two products, A and B, during a given time period. Each of these products requires four different manufacturing operations: grinding, turning, assembling and testing. The manufacturing requirements in hours per unit of products A and B are given below.
| A | B | |
| Grinding | 1 | 2 |
| Turning | 3 | 1 |
| Assembling | 6 | 3 |
| Testing | 5 | 4 |
The available capacities of these operations in hours for the given time period are: grinding 30; turning 60, assembling 200; testing 200. The contribution to profit is Rs 20 for each unit of A and Rs 30 for each unit of B. The firm can sell all that it produces at the prevailing market price. Determine the optimum amount of A and B to produce during the given time period. Formulate this as a LPP.
Vitamins A and B are found in two different foods F1 and F2. One unit of food F1contains 2 units of vitamin A and 3 units of vitamin B. One unit of food F2 contains 4 units of vitamin A and 2 units of vitamin B. One unit of food F1 and F2 cost Rs 50 and 25 respectively. The minimum daily requirements for a person of vitamin A and B is 40 and 50 units respectively. Assuming that any thing in excess of daily minimum requirement of vitamin A and B is not harmful, find out the optimum mixture of food F1 and F2 at the minimum cost which meets the daily minimum requirement of vitamin A and B. Formulate this as a LPP.
An automobile manufacturer makes automobiles and trucks in a factory that is divided into two shops. Shop A, which performs the basic assembly operation, must work 5 man-days on each truck but only 2 man-days on each automobile. Shop B, which performs finishing operations, must work 3 man-days for each automobile or truck that it produces. Because of men and machine limitations, shop A has 180 man-days per week available while shop B has 135 man-days per week. If the manufacturer makes a profit of Rs 30000 on each truck and Rs 2000 on each automobile, how many of each should he produce to maximize his profit? Formulate this as a LPP.
Objective function of a LPP is
Let X1 and X2 are optimal solutions of a LPP, then
The optimal value of the objective function is attained at the points
The maximum value of Z = 4x + 3y subjected to the constraints 3x + 2y ≥ 160, 5x + 2y ≥ 200, x + 2y ≥ 80; x, y ≥ 0 is
Consider a LPP given by
Minimum Z = 6x + 10y
Subjected to x ≥ 6; y ≥ 2; 2x + y ≥ 10; x, y ≥ 0
Redundant constraints in this LPP are
Which of the following is not a convex set?
A company manufactures two types of toys A and B. A toy of type A requires 5 minutes for cutting and 10 minutes for assembling. A toy of type B requires 8 minutes for cutting and 8 minutes for assembling. There are 3 hours available for cutting and 4 hours available for assembling the toys in a day. The profit is ₹ 50 each on a toy of type A and ₹ 60 each on a toy of type B. How many toys of each type should the company manufacture in a day to maximize the profit? Use linear programming to find the solution.
State whether the following is True or False:
The optimum value of the objective function of LPP occurs at the centre of the feasible region.
Choose the correct alternative:
The constraint that in a college there are more scholarship holders in FYJC class (X) than in SYJC class (Y) is given by
Choose the correct alternative:
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The half-plane represented by 3x + 4y ≥ 12 includes the point (4, 3)
Tyco Cycles Ltd manufactures bicycles (x) and tricycles (y). The profit earned from the sales of each bicycle and a tricycle are ₹ 400 and ₹ 200 respectively, then the total profit earned by the manufacturer will be given as ______
Ms. Mohana want to invest at least ₹ 55000 in Mutual funds and fixed deposits. Mathematically this information can be written as ______
Determine the minimum value of Z = 3x + 2y (if any), if the feasible region for an LPP is shown in Figue.
Minimise Z = 3x + 5y subject to the constraints:
x + 2y ≥ 10
x + y ≥ 6
3x + y ≥ 8
x, y ≥ 0
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 ______.
Feasible region (shaded) for a LPP is shown in the Figure Minimum of Z = 4x + 3y occurs at the point ______.
The common region determined by all the linear constraints of a LPP is called the ______ region.
In maximization problem, optimal solution occurring at corner point yields the ____________.
A type of problems which seek to maximise (or, minimise) profit (or cost) form a general class of problems called.
What is defined as a problem in which a linear objective function is to be maximised or minimised subject to a set of linear constraints and non-negative conditions on the variables?
An optimisation problem becomes a Linear Programming Problem (LPP) when:
A furniture dealer invests in tables (\[x\]) and chairs (\[y\]). He has \[\text{Rs } 50,000\] to invest and storage space for at most \[60\] pieces. A table costs \[\text{Rs } 2500\] and gives a profit of \[\text{Rs } 250\], while a chair costs \[\text{Rs } 500\] and gives a profit of \[\text{Rs } 75\]. What is the objective function to maximise total profit \[Z\]?
For a furniture dealer with an investment limit of \[\text{Rs } 50,000\] and space for at most \[60\] pieces, where a table costs \[\text{Rs } 2500\] and a chair costs \[\text{Rs } 500\], which set of inequalities correctly represents the investment and storage constraints (where \[x\] is tables and \[y\] is chairs)?
