CBSE Questions for Class 12 Commerce Maths Linear Programming Quiz 3 - MCQExams.com

Choose the most correct of the following statements relating to primal-dual linear programming problems:
  • Shadow prices of resources in the primal are optimal values of the dual variables.
  • The optimal values of the objective functions of primal and dual are the same.
  • If the primal problem has unbounded solution, the dual problem would have infeasibility.
  • All of the above.
To write the dual; it should be ensured that  
I. All the primal variables are non-negative.
II. All the bi values are non-negative.
III. All the constraints are $$≤$$ type if it is maximization problem and $$≥$$ type if it is a minimization problem.
  • I and II
  • II and III
  • I and III
  • I, II and III
Mark the wrong statement:
  • The primal and dual have equal number of variables.
  • The shadow price indicates the change in the value of the objective function, per unit increase in the value of the RHS.
  • The shadow price of a non-binding constraint is always equal to zero.
  • The information about shadow price of a constraint is important since it may be possible to purchase or, otherwise, acquire additional units of the concerned resource.
Which of the following statements about an LP problem and its dual is false?
  • If the primal and the dual both have optimal solutions, the objective function values for both problems are equal at the optimum
  • If one of the variables in the primal has unrestricted sign, the corresponding constraint in the dual is satisfied with equality
  • If the primal has an optimal solution, so has the dual
  • The dual problem might have an optimal solution, even though the primal has no (bounded) optimum
LP theory states that the optimal solution to any problem will lie at
  • the origin.
  • a corner point of the feasible region.
  • the highest point of the feasible region.
  • the lowest point in the feasible region.
  • none of the above
Unboundedness is usually a sign that the LP problem.
  • has finite multiple solutions.
  • is degenerate.
  • contains too many redundant constraints.
  • has been formulated improperly.
  • none of the above.
An objective function in a linear program can be which of the following?
  • A maximization function
  • A nonlinear maximization function
  • A quadratic maximization function
  • An uncertain quantity
  • A divisible additive function
A point that satisfies all of a problem's constraints simultaneously is $$a(n)$$
  • maximum profit point.
  • corner point.
  • intersection of the profit line and a constraint.
  • intersection of two or more constraints.
  • None of the above
Feasible region's optimal solution for a linear objective function always includes
  • downward point
  • upward point
  • corner point
  • front point
While plotting constraints on a graph paper, terminal points on both the axes are connected by a straight line because:
  • the resources are limited in supply
  • the objective function as a linear function
  • the constraints are linear equations or inequalities
  • all of the above
In linear programming context, sensitivity analysis is a technique to
  • Allocate resources optimally.
  • Minimize cost of operations.
  • Spell out relation between primal and dual.
  • Determine how optimal solution to LPP changes in response to problem inputs.
Which of the following is an essential condition in a situation for linear programming to be useful?
  • Linear constraints
  • Bottlenecks in the objective function
  • Non-homogeneity
  • Uncertainty
  • None of the above
Apply linear programming to this problem. A firm wants to determine how many units of each of two products (products D and E) they should produce to make the most money. The profit in the manufacture of a unit of product D is $100 and the profit in the manufacture of a unit of product E is $The firm is limited by its total available labor hours and total available machine hours. The total labor hours per week are 4,Product D takes 5 hours per unit of labor and product E takes 7 hours per unit. The total machine hours are 5,000 per week. Product D takes 9 hours per unit of machine time and product E takes 3 hours per unit. Which of the following is one of the constraints for this linear program?
  • $$5 D + 7 E≤ 5,000$$
  • $$9 D + 3 E ≥4,000$$
  • $$5 D + 7 E = 4,000$$
  • $$5 D + 9 E ≤5,000$$
  • $$9 D + 3 E ≤5,000$$
A constraint in an LP model becomes redundant because:
  • two iso-profit line may be parallel to each other
  • the solution is unbounded
  • this constraint is not satisfied by the solution values
  • none of the above
If two constraints do not intersect in the positive quadrant of the graph, then
  • The problem is infeasible
  • The solution is unbounded
  • One of the constraints is redundant
  • None of the above
In profit objective function, all lines representing same level of profit are classified as
  • iso-objective lines
  • iso-function lines
  • iso-profit lines
  • iso-cost lines
The number of constraints allowed in a linear program is which of the following?
  • Less than 5
  • Less than 72
  • Less than 512
  • Less than 1,024
  • Unlimited
A feasible solution to an LP problem
  • must satisfy all of the problems constraints simultaneously
  • need not satisfy all of the constraints, only some of them
  • must be a corner point of the feasible region
  • must optimize the value of the objective function
In North west corner rule if the demand in the column is satisfied one must move to the 
  • left cell in the next column
  • right cell in the next row
  • right cell in the next column
  • left cell in the next row
The __________ is the method available for solving an L.P.P
  • graphical method
  • least cost method
  • MODI method
  • Hungarian method
In North west corner rule, if the supply in the row is satisfied one must move 
  • down in the next row
  • up in the next row
  • right cell in the next column
  • left cell in the next row
In North west corner rule the allocation is done in 
  • upper left corner
  • upper right corner
  • middle cell in the transportation table
  • cell with the lowest cost.
In Graphical solution the feasible solution is any solution to a LPP which satisfies 
  • only objective function.
  • non-negativity restriction.
  • only constraint.
  • all the three
Which of the following is not true about feasibility?
  • It cannot be determined in a graphical solution of an LPP
  • It is independent of the objective function
  • It implies that there must be a convex region satisfying all the constraints
  • Extreme points of the convex region gives the optimum solution.
In Graphical solution the redundant constraint is
  • which forms the boundary of feasible region.
  • which do not optimizes the objective function.
  • which does not form boundary of feasible region
  • which optimizes the objective function.
In a graphical solution, the feasible region is:
  • where all the constraints are satisfied simultaneously.
  • any one constraint is satisfied.
  • only the first constraint is satisfied.
  • any one of the above condition.
One disadvantage of using North-West Corner rule to find initial solution to the transportation problem is that
  • It is complicated to use
  • It does not take into account cost of transportation
  • It leads to a degenerate initial solution
  • All of the above
One disadvantage of using north west corner rule to find initial solution to the transportation problem is that
  • it is difficult to use.
  • it does not take into account cost of transportation.
  • it leads to a degenerate initial solution.
  • .transportation cost is maximum.
Which of the following is not a corner point $$(x,y)$$ in the formulation of the given LPP?
  • $$(100,100)$$
  • $$(200,170)$$
  • $$(200,100)$$
  • $$(150,100)$$
A farmer has $$10$$ acres of land to plant wheat and rye. He has to plant atleast $$7$$ acres. Each acre of wheat costs $$\$200$$ and each acre of rye costs $$\$100$$ to plant. He has only $$\$1200$$ to spend. Moreover, the farmer has to get the planting done in $$12$$ hours and it takes $$1$$ hour to plant an acre of wheat and $$2$$ hours to plant an acre of rye. An acre of wheat yields a profit of $$\$500$$ and an acre of rye yields a profit of $$\$300$$.

$$($$Take $$x$$ and $$y$$ as the acres of wheat and rye planted respectively$$)$$. What is the maximum profit that the farmer can make?
  • $$\$2500$$
  • $$\$2800$$
  • $$\$3100$$
  • $$\$3200$$
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