English

The region represented by the inequalities x ≥ 0, y ≥ 0 lies in first quadrant. - Mathematics and Statistics

Advertisements
Advertisements

Question

The region represented by the inequalities x ≥ 0, y ≥ 0 lies in first quadrant.

Options

  • True

  • False

MCQ
True or False

Solution

The given statement is True.

shaalaa.com
  Is there an error in this question or solution?
Chapter 6: Linear Programming - Miscellaneous Exercise 6 [Page 104]

APPEARS IN

Balbharati Mathematics and Statistics 2 (Commerce) [English] 12 Standard HSC Maharashtra State Board
Chapter 6 Linear Programming
Miscellaneous Exercise 6 | Q 3.1 | Page 104

RELATED QUESTIONS

Amit's mathematics teacher has given him three very long lists of problems with the instruction to submit not more than 100 of them (correctly solved) for credit. The problem in the first set are worth 5 points each, those in the second set are worth 4 points each, and those in the third set are worth 6 points each. Amit knows from experience that he requires on the average 3 minutes to solve a 5 point problem, 2 minutes to solve a 4 point problem, and 4 minutes to solve a 6 point problem. Because he has other subjects to worry about, he can not afford to devote more than

\[3\frac{1}{2}\] hours altogether to his mathematics assignment. Moreover, the first two sets of problems involve numerical calculations and he knows that he cannot stand more than 
\[2\frac{1}{2}\]  hours work on this type of problem. Under these circumstances, how many problems in each of these categories shall he do in order to get maximum possible credit for his efforts? Formulate this as a LPP.

 


The corner points of the feasible region determined by the following system of linear inequalities:
2x + y ≤ 10, x + 3y ≤ 15, xy ≥ 0 are (0, 0), (5, 0), (3, 4) and (0, 5). Let Z = px + qy, where p, q > 0. Condition on p and q so that the maximum of Z occurs at both (3, 4) and (0, 5) is 


Solve the following L.P.P. by graphical method:

Maximize: Z = 10x + 25y
subject to 0 ≤ x ≤ 3,
0 ≤ y ≤ 3,
x + y ≤ 5.
Also find the maximum value of z.


Solve the following L.P.P. by graphical method:

Minimize: Z = 6x + 2y subject to x + 2y ≥ 3, x + 4y ≥ 4, 3x + y ≥ 3, x ≥ 0, y ≥ 0.


Choose the correct alternative:

The value of objective function is maximize under linear constraints.


State whether the following is True or False :

The region represented by the inqualities x ≤ 0, y ≤ 0 lies in first quadrant.


Solve the following problem :

Maximize Z = 4x1 + 3x2 Subject to 3x1 + x2 ≤ 15, 3x1 + 4x2 ≤ 24, x1 ≥ 0, x2 ≥ 0


Solve the following problem :

A company manufactures bicyles and tricycles, each of which must be processed through two machines A and B Maximum availability of machine A and B is respectively 120 and 180 hours. Manufacturing a bicycle requires 6 hours on machine A and 3 hours on machine B. Manufacturing a tricycle requires 4 hours on machine A and 10 hours on machine B. If profits are ₹ 180 for a bicycle and ₹ 220 on a tricycle, determine the number of bicycles and tricycles that should be manufacturing in order to maximize the profit.


Solve the following problem :

A factory produced two types of chemicals A and B The following table gives the units of ingredients P & Q (per kg) of Chemicals A and B as well as minimum requirements of P and Q and also cost per kg. of chemicals A and B.

Ingredients per kg. /Chemical Units A
(x)
B
(y)
Minimum requirements in
P 1 2 80
Q 3 1 75
Cost (in ₹) 4 6  

Find the number of units of chemicals A and B should be produced so as to minimize the cost.


State whether the following statement is True or False:

If LPP has two optimal solutions, then the LPP has infinitely many solutions


State whether the following statement is True or False:

A convex set includes the points but not the segment joining the points


State whether the following statement is True or False:

If the corner points of the feasible region are `(0, 7/3)`, (2, 1), (3, 0) and (0, 0), then the maximum value of Z = 4x + 5y is 12


State whether the following statement is True or False:

Of all the points of feasible region, the optimal value is obtained at the boundary of the feasible region


A company manufactures 2 types of goods P and Q that requires copper and brass. Each unit of type P requires 2 grams of brass and 1 gram of copper while one unit of type Q requires 1 gram of brass and 2 grams of copper. The company has only 90 grams of brass and 80 grams of copper. Each unit of types P and Q brings profit of ₹ 400 and ₹ 500 respectively. Find the number of units of each type the company should produce to maximize its profit


A wholesale dealer deals in two kinds of mixtures A and B of nuts. Each kg of mixture A contains 60 grams of almonds, 30 grams of cashew and 30 grams of hazel nuts. Each kg of mixture B contains 30 grams of almonds, 60 grams of cashew and 180 grams of hazel nuts. A dealer is contemplating to use mixtures A and B to make a bag which will contain at least 240 grams of almonds, 300 grams of cashew and 540 grams of hazel nuts. Mixture A costs ₹ 8 and B costs ₹ 12 per kg. How many kgs of each mixture should he use to minimize the cost of the kgs


Maximize Z = 400x + 500y subject to constraints

x + 2y ≤ 80, 2x + y ≤ 90, x ≥ 0, y ≥ 0


A linear function z = ax + by, where a and b are constants, which has to be maximised or minimised according to a set of given condition is called a:-


Graphical solution set of the inequations x ≥ 0 and y ≤ 0 lies in ______ quadrant.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×