12th Standard cbse -- Maths - Linear Programming

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Question - 1

Of all the points of the feasible region, for maximum or minimum of objective function, the point lies

  • A inside the feasible region
  • B at the boundary line of the feasible region
  • C vertex point of the boundary of the feasible region
  • D none of these

Question - 2

A dealer wishes to purchase a number of fans and sewing machines. He has only Rs. 5,760 to invest and has space for at most 20 items. A fan costs him Rs. 360 and a sewing machine Rs. 240. He expects to sell a fan at a profit of Rs. 22 and a sewing machine at a profit of Rs. 18. Assinning that he can sell all the items that he buys, how should he invests his money to maximise the profit? The LPP for above question is

  • A x → fans, y → sewing machines To maximise Z = 22x + 18y subject to constraints x ≥ 0, y ≥ 0, x + y ≤ 20 360x + 240y ≥ 5760
  • B x → fans, y → sewing machines To maximise Z= 18x + 22y subject to constraints x ≥ 0, y ≥ 0, x + y ≤ 20 360x + 240y ≥ 5760
  • C x → fans, y → sewing machines To maximise Z = 22x + 18y x ≥ 0, y ≥ 0, x + y ≥ 0 360x + 240y ≥ 5760
  • D x → fans, y → sewing machines To maximise Z = 22x + 18j x ≥ 0, y ≥ 0, x + y ≤ 20 360x + 240y ≤ 5760

Question - 3

Feasible region is the set of points which satisfy

  • A the objective functions
  • B some of the given constraints
  • C all of the given constraints
  • D none of these

Question - 4

An aeroplane can carry a maximum of 200 passangers. A profit of  Rs. 400 is made on each first class ticket and a profit of Rs. 300 is made on each economy class ticket. An airline reserves at least 20 seats for first class. However, at least 4 times as many passengers prefer to travel by economy class than by first class. Find how many tickets of each type must be sold to maximise the profit? The LPP for the given situation is

  • A x → first class, y → economy class To maximise Z = 400x + 300y subject to constraints x ≥ 0, y ≥ 0, x+y ≤ 200 x ≥ 20, y ≥ 80
  • B x → first class, y → economy class To maximise Z 400x + 300y subject to constraints x ≥ 0, y ≥ 0, x+y ≥ 200 x ≥ 20, y ≥ 80
  • C x → first class, y → economy class To maximise Z = 400x + 300y subject to constraints x ≥ 0, y ≥ 0, x ≥ 20 x + y ≤ 200 x ≥ 4y
  • D x → first class, y → economy class To maximise Z = 400x + 300y subject to constraints x ≥ 20, y ≥ 0 x + y ≤ 200 y ≥ 4x

Question - 5

Problems which seek to maximise or, minimise profit or, cost form a general class of problems called ………

  • A Simple problems
  • B Difficult problems
  • C Non-linear problems
  • D Optimisation problems

Question - 6

A ……… of a feasible region is a point in the region, which is the intersection of two boundary lines.

  • A Section point
  • B Corner point
  • C Reasonable point
  • D Vertex point

Question - 7

The linear inequalities or equations or restrictions on the variables of a linear programming problem are called …… The conditions x ≥ 0 , y ≥ 0 are called …….

  • A Objective functions, optimal value
  • B Constraints, non-negative restrictions
  • C Objective functions, non-negative restrictions
  • D Constraints, negative restrictions

Question - 8

The common region determined by all the constraints including non-negative constraints x, y ≥ 0 of a linear programming problem is called the ………

  • A Bounded region
  • B Simple region
  • C Infeasible region
  • D Feasible region

Question - 9

Let Z = ax + by is a linear objective function. Variables x and y are called ……… variables.

  • A Independent
  • B Continuous
  • C Decision
  • D Dependent

Question - 10

A linear function of several variables x and y is called ………

  • A Non-linear function
  • B Optimal function
  • C Objective function
  • D Simple function
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