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State whether the following is True or False : The region represented by the inqualities x ≤ 0, y ≤ 0 lies in first quadrant. - Mathematics and Statistics

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प्रश्न

State whether the following is True or False :

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

विकल्प

  • True

  • False

MCQ
सत्य या असत्य
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उत्तर

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

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अध्याय 6: Linear Programming - Miscellaneous Exercise 6 [पृष्ठ १०४]

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बालभारती Mathematics and Statistics 2 (Commerce) [English] Standard 12 Maharashtra State Board
अध्याय 6 Linear Programming
Miscellaneous Exercise 6 | Q 3.2 | पृष्ठ १०४

संबंधित प्रश्न

A firm manufactures 3 products AB and C. The profits are Rs 3, Rs 2 and Rs 4 respectively. The firm has 2 machines and below is the required processing time in minutes for each machine on each product : 

Machine Products
A B C
M1
M2
4 3 5
2 2 4

Machines M1 and M2 have 2000 and 2500 machine minutes respectively. The firm must manufacture 100 A's, 200 B's and 50 C's but not more than 150 A's. Set up a LPP to maximize the profit.


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 


A firm manufactures two products, each of which must be processed through two departments, 1 and 2. The hourly requirements per unit for each product in each department, the weekly capacities in each department, selling price per unit, labour cost per unit, and raw material cost per unit are summarized as follows:
 

  Product A Product B Weekly capacity
Department 1 3 2 130
Department 2 4 6 260
Selling price per unit ₹ 25 ₹ 30  
Labour cost per unit ₹ 16 ₹ 20  
Raw material cost per unit ₹ 4 ₹ 4  


The problem is to determine the number of units to produce each product so as to maximize total contribution to profit. Formulate this as a LPP.


Choose the correct alternative:

The value of objective function is maximize under linear constraints.


Choose the correct alternative :

The maximum value of z = 5x + 3y. subject to the constraints


Choose the correct alternative :

The maximum value of z = 10x + 6y, subjected to the constraints 3x + y ≤ 12, 2x + 5y ≤ 34, x ≥ 0, y ≥ 0 is.


Fill in the blank :

Graphical solution set of the in equations x ≥ 0, y ≥ 0 is in _______ quadrant


Fill in the blank :

The region represented by the in equations x ≤ 0, y ≤ 0 lines in _______ quadrants.


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


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 the availability of each machine is given by the following table.

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

Formulate and solve the following Linear programming problems using graphical method.


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.


Solve the following problem :

A Company produces mixers and processors Profit on selling one mixer and one food processor is ₹ 2000 and ₹ 3000 respectively. Both the products are processed through three machines A, B, C The time required in hours by each product and total time available in hours per week on each machine are as follows:

Machine/Product Mixer per unit Food processor per unit Available time
A 3 3 36
B 5 2 50
C 2 6 60

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


Solve the following problem :

A person makes two types of gift items A and B requiring the services of a cutter and a finisher. Gift item A requires 4 hours of cutter's time and 2 hours of finisher's time. B requires 2 hours of cutters time, 4 hours of finishers time. The cutter and finisher have 208 hours and 152 hours available times respectively every month. The profit of one gift item of type A is ₹ 75 and on gift item B is ₹ 125. Assuming that the person can sell all the items produced, determine how many gift items of each type should be make every month to obtain the best returns?


Solve the following problem :

A firm manufacturing two types of electrical items A and B, can make a profit of ₹ 20 per unit of A and ₹ 30 per unit of B. Both A and B make use of two essential components, a motor and a transformer. Each unit of A requires 3 motors and 2 transformers and each unit of B requires 2 motors and 4 transformers. The total supply of components per month is restricted to 210 motors and 300 transformers. How many units of A and B should be manufacture per month to maximize profit? How much is the maximum profit?


Choose the correct alternative:

If LPP has optimal solution at two point, then


Choose the correct alternative:

The maximum value of Z = 3x + 5y subjected to the constraints x + y ≤ 2, 4x + 3y ≤ 12, x ≥ 0, y ≥ 0 is


Choose the correct alternative:

The point at which the minimum value of Z = 8x + 12y subject to the constraints 2x + y ≥ 8, x + 2y ≥ 10, x ≥ 0, y ≥ 0 is obtained at the point


Choose the correct alternative:

The corner points of feasible region for the inequations, x + y ≤ 5, x + 2y ≤ 6, x ≥ 0, y ≥ 0 are


Choose the correct alternative:

The corner points of the feasible region are (0, 3), (3, 0), (8, 0), `(12/5, 38/5)` and (0, 10), then the point of maximum Z = 6x + 4y = 48 is at


Choose the correct alternative:

The corner points of the feasible region are (4, 2), (5, 0), (4, 1) and (6, 0), then the point of minimum Z = 3.5x + 2y = 16 is at


State whether the following statement is True or False:

The maximum value of Z = 5x + 3y subjected to constraints 3x + y ≤ 12, 2x + 3y ≤ 18, 0 ≤ x, y is 20


State whether the following statement is True or False:

The graphical solution set of the inequations 0 ≤ y, x ≥ 0 lies in second quadrant


If the feasible region is bounded by the inequations 2x + 3y ≤ 12, 2x + y ≤ 8, 0 ≤ x, 0 ≤ y, then point (5, 4) is a ______ of the feasible region


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 = 2x + 3y subject to constraints

x + 4y ≤ 8, 3x + 2y ≤ 14, x ≥ 0, y ≥ 0.


Maximize Z = 400x + 500y subject to constraints

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


Shraddho wants to invest at most ₹ 25,000/- in saving certificates and fixed deposits. She wants to invest at least ₹ 10,000/- in saving certificate and at least ₹ 15,000/- in fixed deposits. The rate of interest on saving certificate is 5% and that on fixed deposits is 7% per annum. Formulate the above problem as LPP to determine maximum income yearly.


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


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