मराठी
महाराष्ट्र राज्य शिक्षण मंडळएचएससी विज्ञान (सामान्य) इयत्ता १२ वी

Solve each of the following inequations graphically using XY-plane: 5y - 12 ≥ 0 - Mathematics and Statistics

Advertisements
Advertisements

प्रश्न

Solve each of the following inequations graphically using XY-plane:

5y - 12 ≥ 0

आलेख
बेरीज
Advertisements

उत्तर

Consider the line whose equation is 5y - 12 ≥ 0 i.e. y = `12/5`

This represents a line parallel to X-axis passing3through the point `(0, 12/5)`

Draw the line y = `12/5`

To find the solution set, we have to check the position of the origin (0, 0).

When y = 0,  5y - 12 = 5(0) - 12 = - 12 > 0

∴ the coordinates of the origin does not satisfy the given inequality.

∴ the solution set consists of the line y = `12/5` and the non-origin side of the line which is shaded in the graph.

shaalaa.com
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 7: Linear Programming - Miscellaneous exercise 7 [पृष्ठ २४३]

APPEARS IN

बालभारती Mathematics and Statistics 1 (Arts and Science) [English] Standard 12 Maharashtra State Board
पाठ 7 Linear Programming
Miscellaneous exercise 7 | Q II) 1) iii) | पृष्ठ २४३

संबंधित प्रश्‍न

Find the feasible solution of the following inequation:

x + 4y ≤ 24, 3x + y ≤ 21, x + y ≤ 9,  x ≥ 0, y ≥ 0.


A company manufactures two types of chemicals Aand B. Each chemical requires two types of raw material P and Q. The table below shows number of units of P and Q required to manufacture one unit of A and one unit of B and the total availability of P and Q.

Chemical→ A B Availability
Raw Material ↓
P 3 2 120
Q 2 5 160

The company gets profits of ₹ 350 and ₹ 400 by selling one unit of A and one unit of B respectively. (Assume that the entire production of A and B can be sold). How many units of the chemicals A and B should be manufactured so that the company gets a maximum profit? Formulate the problem as LPP to maximize profit.


A doctor has prescribed two different units of foods A and B to form a weekly diet for a sick person. The minimum requirements of fats, carbohydrates and proteins are 18, 28, 14 units respectively. One unit of food A has 4 units of fat, 14 units of carbohydrates and 8 units of protein. One unit of food B has 6 units of fat, 12 units of carbohydrates and 8 units of protein. The price of food A is ₹ 4.5 per unit and that of food B is ₹ 3.5 per unit. Form the LPP, so that the sick person’s diet meets the requirements at a minimum cost.


Solve the following LPP by graphical method:

Maximize z = 7x + 11y, subject to 3x + 5y ≤ 26, 5x + 3y ≤ 30, x ≥ 0, y ≥ 0.


The corner points of the feasible solution are (0, 0), (2, 0), `(12/7, 3/7)`, (0, 1). Then z = 7x + y is maximum at ______.


The half-plane represented by 4x + 3y >14 contains the point ______.


Solve the following LPP:

Maximize z = 2x + 3y subject to x - y ≥ 3, x ≥ 0, y ≥ 0.


Solve each of the following inequations graphically using XY-plane:

4x - 18 ≥ 0


Solve each of the following inequations graphically using XY-plane:

- 11x - 55 ≤ 0


Solve the following LPP:

Maximize z = 4x1 + 3x2 subject to
3x1 + x2 ≤ 15, 3x1 + 4x2 ≤ 24, x1 ≥ 0, x2 ≥ 0. 


A carpenter makes chairs and tables. Profits are ₹ 140 per chair and ₹ 210 per table. Both products are processed on three machines: Assembling, Finishing and Polishing. The time required for each product in hours and availability of each machine is given by the following table:

Product → Chair (x) Table (y) Available time (hours)
Machine ↓
Assembling 3 3 36
Finishing 5 2 50
Polishing 2 6 60

Formulate the above problem as LPP. Solve it graphically


A company produces mixers and food processors. Profit on selling one mixer and one food processor is Rs 2,000 and Rs 3,000 respectively. Both the products are processed through three machines A, B, C. The time required in hours for each product and total time available in hours per week on each machine arc as follows:

Machine  Mixer Food Processor Available time
A 3 3 36
B 5 2 50
C 2 6 60

How many mixers and food processors should be produced in order to maximize the profit?


A firm manufactures two products A and B on which profit earned per unit are ₹ 3 and ₹ 4 respectively. Each product is processed on two machines M1 and M2. The product A requires one minute of processing time on M1 and two minutes of processing time on M2, B requires one minute of processing time on M1 and one minute of processing time on M2. Machine M1 is available for use for 450 minutes while M2 is available for 600 minutes during any working day. Find the number of units of products A and B to be manufactured to get the maximum profit.


A company manufactures two types of chemicals A and B. Each chemical requires two types of raw material P and Q. The table below shows number of units of P and Q required to manufacture one unit of A and one unit of B.

Raw Material \Chemical A B Availability
p 3 2 120
Q 2 5 160

The company gets profits of ₹ 350 and ₹ 400 by selling one unit of A and one unit of B respectively. Formulate the problem as L.P.P. to maximize the profit.


A company manufactures two types of fertilizers F1 and F2. Each type of fertilizer requires two raw materials A and B. The number of units of A and B required to manufacture one unit of fertilizer F1 and F2 and availability of the raw materials A and B per day are given in the table below:

Raw Material\Fertilizers F1 F2 Availability
A 2 3 40
B 1 4 70

By selling one unit of F1 and one unit of F2, company gets a profit of ₹ 500 and ₹ 750 respectively. Formulate the problem as L.P.P. to maximize the profit.


Objective function of LPP is ______.


Fill in the blank :

A dish washing machine holds up to 40 pieces of large crockery (x) This constraint is given by_______.


State whether the following is True or False :

The point (1, 2) is not a vertex of the feasible region bounded by 2x + 3y ≤ 6, 5x + 3y ≤ 15, x ≥ 0, y ≥ 0.


The point of which the maximum value of z = x + y subject to constraints x + 2y ≤ 70, 2x + y ≤ 90, x ≥ 0, y ≥ 0 is obtained at


Which value of x is in the solution set of inequality − 2X + Y ≥ 17


Maximize z = 5x + 2y subject to 3x + 5y ≤ 15, 5x + 2y ≤ 10, x ≥ 0, y ≥ 0


Maximize z = 10x + 25y subject to x + y ≤ 5, 0 ≤ x ≤ 3, 0 ≤ y ≤ 3


Solve the Linear Programming problem graphically:

Maximize z = 3x + 5y subject to x + 4y ≤ 24, 3x + y ≤ 21, x + y ≤ 9, x ≥ 0, y ≥ 0 also find the maximum value of z.


Minimize z = 7x + y subjected to 5x + y ≥ 5, x + y ≥ 3, x ≥ 0, y ≥ 0.


Maximize z = −x + 2y subjected to constraints x + y ≥ 5, x ≥ 3, x + 2y ≥ 6, y ≥ 0 is this LPP solvable? Justify your answer.


State whether the following statement is True or False:

Objective function of LPP is a relation between the decision variables


The variables involved in LPP are called ______


A company produces two types of pens A and B. Pen A is of superior quality and pen B is of lower quality. Profits on pens A and B are ₹ 5 and ₹ 3 per pen respectively. Raw materials required for each pen A is twice as that of pen B. The supply of raw material is sufficient only for 1000 pens per day. Pen A requires a special clip and only 400 such clips are available per day. For pen B, only 700 clips are available per day. Formulate this problem as a linear programming problem.


Solve the following linear programming problems by graphical method.

Maximize Z = 6x1 + 8x2 subject to constraints 30x1 + 20x2 ≤ 300; 5x1 + 10x2 ≤ 110; and x1, x2 ≥ 0.


Solve the following linear programming problems by graphical method.

Maximize Z = 20x1 + 30x2 subject to constraints 3x1 + 3x2 ≤ 36; 5x1 + 2x2 ≤ 50; 2x1 + 6x2 ≤ 60 and x1, x2 ≥ 0.


Solve the following linear programming problems by graphical method.

Minimize Z = 20x1 + 40x2 subject to the constraints 36x1 + 6x2 ≥ 108; 3x1 + 12x2 ≥ 36; 20x1 + 10x2 ≥ 100 and x1, x2 ≥ 0.


A solution which maximizes or minimizes the given LPP is called


A firm manufactures two products A and B on which the profits earned per unit are ₹ 3 and ₹ 4 respectively. Each product is processed on two machines M1 and M2. Product A requires one minute of processing time on M1 and two minutes on M2, While B requires one minute on M1 and one minute on M2. Machine M1 is available for not more than 7 hrs 30 minutes while M2 is available for 10 hrs during any working day. Formulate this problem as a linear programming problem to maximize the profit.


Solve the following linear programming problem graphically.

Maximize Z = 60x1 + 15x2 subject to the constraints: x1 + x2 ≤ 50; 3x1 + x2 ≤ 90 and x1, x2 ≥ 0.


The LPP to maximize Z = x + y, subject to x + y ≤ 1, 2x + 2y ≥ 6, x ≥ 0, y ≥ 0 has ________.


The values of θ satisfying sin7θ = sin4θ - sinθ and 0 < θ < `pi/2` are ______


The point which provides the solution of the linear programming problem, Max.(45x + 55y) subject to constraints x, y ≥ 0, 6x + 4y ≤ 120, 3x + 10y ≤ 180, is ______ 


Solution which satisfy all constraints is called ______ solution.


Find graphical solution for the following system of linear in equation:

x + 2y ≥ 4, 2x - y ≤ 6


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×