English

In a LPP, the maximum value of the objective function Z = ax + by is always finite.

Advertisements
Advertisements

Question

In a LPP, the maximum value of the objective function Z = ax + by is always finite.

Options

  • True

  • False

MCQ
True or False
Advertisements

Solution

This statement is True.

shaalaa.com
  Is there an error in this question or solution?
Chapter 12: Linear Programming - Exercise [Page 257]

APPEARS IN

NCERT Exemplar Mathematics Exemplar [English] Class 12
Chapter 12 Linear Programming
Exercise | Q 45 | Page 257

RELATED QUESTIONS

Solve the following Linear Programming Problems graphically:

Minimise Z = – 3x + 4 y

subject to x + 2y ≤ 8, 3x + 2y ≤ 12, x ≥ 0, y ≥ 0.


Solve the following Linear Programming Problems graphically:

Minimise Z = x + 2y

subject to 2x + y ≥ 3, x + 2y ≥ 6, x, y ≥ 0.


Show that the minimum of Z occurs at more than two points.

Minimise and Maximise Z = 5x + 10 y

subject to x + 2y ≤ 120, x + y ≥ 60, x – 2y ≥ 0, x, y ≥ 0.


A dietician wishes to mix together two kinds of food X and Y in such a way that the mixture contains at least 10 units of vitamin A, 12 units of vitamin B and 8 units of vitamin C. The vitamin content of one kg food is given below:

Food Vitamin A Vitamin B Vitamin C
X 1 2 3
Y 2 2 1

One kg of food X costs Rs 16 and one kg of food Y costs Rs 20. Find the least cost of the mixture which will produce the required diet?

 


An aeroplane can carry a maximum of 200 passengers. A profit of Rs 1000 is made on each executive class ticket and a profit of Rs 600 is made on each economy class ticket. The airline reserves at least 20 seats for executive class. However, at least 4 times as many passengers prefer to travel by economy class than by the executive class. Determine how many tickets of each type must be sold in order to maximize the profit for the airline. What is the maximum profit?


A small firm manufactures necklaces and bracelets. The total number of necklaces and bracelets that it can handle per day is at most 24. It takes one hour to make a bracelet and half an hour to make a necklace. The maximum number of hours available per day is 16. If the profit on a necklace is Rs 100 and that on a bracelet is Rs 300. Formulate on L.P.P. for finding how many of each should be produced daily to maximize the profit?

It is being given that at least one of each must be produced.


If the feasible region for a linear programming problem is bounded, then the objective function Z = ax + by has both a maximum and a minimum value on R.


The minimum value of the objective function Z = ax + by in a linear programming problem always occurs at only one corner point of the feasible region


Maximise Z = 3x + 4y, subject to the constraints: x + y ≤ 1, x ≥ 0, y ≥ 0


Minimise Z = 13x – 15y subject to the constraints: x + y ≤ 7, 2x – 3y + 6 ≥ 0, x ≥ 0, y ≥ 0


The feasible region for a LPP is shown in Figure. Find the minimum value of Z = 11x + 7y


In figure, the feasible region (shaded) for a LPP is shown. Determine the maximum and minimum value of Z = x + 2y.


A man rides his motorcycle at the speed of 50 km/hour. He has to spend Rs 2 per km on petrol. If he rides it at a faster speed of 80 km/hour, the petrol cost increases to Rs 3 per km. He has atmost Rs 120 to spend on petrol and one hour’s time. He wishes to find the maximum distance that he can travel. Express this problem as a linear programming problem


Refer to question 13. Solve the linear programming problem and determine the maximum profit to the manufacturer


A manufacturer produces two Models of bikes-Model X and Model Y. Model X takes a 6 man-hours to make per unit, while Model Y takes 10 man-hours per unit. There is a total of 450 man-hour available per week. Handling and Marketing costs are Rs 2000 and Rs 1000 per unit for Models X and Y respectively. The total funds available for these purposes are Rs 80,000 per week. Profits per unit for Models X and Y are Rs 1000 and Rs 500, respectively. How many bikes of each model should the manufacturer produce so as to yield a maximum profit? Find the maximum profit.


In order to supplement daily diet, a person wishes to take some X and some wishes Y tablets. The contents of iron, calcium and vitamins in X and Y (in milligrams per tablet) are given as below:

Tablets Iron Calcium Vitamin
X 6 3 2
Y 2 3 4

The person needs atleast 18 milligrams of iron, 21 milligrams of calcium and 16 milligrams of vitamin. The price of each tablet of X and Y is Rs 2 and Rs 1 respectively. How many tablets of each should the person take in order to satisfy the above requirement at the minimum cost?


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

Column A Column B
Maximum of Z 325

The feasible solution for a LPP is shown in Figure. Let Z = 3x – 4y be the objective function. Minimum of Z occurs at ______.


Refer to Question 32, Maximum of F – Minimum of F = ______.


If the feasible region for a LPP is ______ then the optimal value of the objective function Z = ax + by may or may not exist.


A feasible region of a system of linear inequalities is said to be ______ if it can be enclosed within a circle.


A corner point of a feasible region is a point in the region which is the ______ of two boundary lines.


In a linear programming problem, the constraints on the decision variables x and y are x − 3y ≥ 0, y ≥ 0, 0 ≤ x ≤ 3. The feasible region:


The maximum value of the object function Z = 5x + 10 y subject to the constraints x + 2y ≤ 120, x + y ≥ 60, x - 2y ≥ 0, x ≥ 0, y ≥ 0 is ____________.


In linear programming, optimal solution ____________.


A maximum or a minimum may not exist for a linear programming problem if ____________.


In Corner point method for solving a linear programming problem, one finds the feasible region of the linear programming problem, determines its corner points, and evaluates the objective function Z = ax + by at each corner point. Let M and m respectively be the largest and smallest values at corner points. In case the feasible region is unbounded, m is the minimum value of the objective function.


Maximize Z = 3x + 5y, subject to x + 4y ≤ 24, 3x + y ≤ 21, x + y ≤ 9, x ≥ 0, y ≥ 0.


Maximize Z = 6x + 4y, subject to x ≤ 2, x + y ≤ 3, -2x + y ≤ 1, x ≥ 0, y ≥ 0.


Z = 6x + 21 y, subject to x + 2y ≥ 3, x + 4y ≥ 4, 3x + y ≥ 3, x ≥ 0, y ≥ 0. The minimum value of Z occurs at ____________.


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


Which statement defines an Optimisation Problem?


Linear Programming is a method of optimisation under which type of constraints?


What are restrictions on decision variables called in linear programming?


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×