Test: Linear Programming (CBSE Level) - 2 - JEE MCQ

# Test: Linear Programming (CBSE Level) - 2 - JEE MCQ

Test Description

## 25 Questions MCQ Test Mathematics (Maths) Class 12 - Test: Linear Programming (CBSE Level) - 2

Test: Linear Programming (CBSE Level) - 2 for JEE 2024 is part of Mathematics (Maths) Class 12 preparation. The Test: Linear Programming (CBSE Level) - 2 questions and answers have been prepared according to the JEE exam syllabus.The Test: Linear Programming (CBSE Level) - 2 MCQs are made for JEE 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Test: Linear Programming (CBSE Level) - 2 below.
Solutions of Test: Linear Programming (CBSE Level) - 2 questions in English are available as part of our Mathematics (Maths) Class 12 for JEE & Test: Linear Programming (CBSE Level) - 2 solutions in Hindi for Mathematics (Maths) Class 12 course. Download more important topics, notes, lectures and mock test series for JEE Exam by signing up for free. Attempt Test: Linear Programming (CBSE Level) - 2 | 25 questions in 25 minutes | Mock test for JEE preparation | Free important questions MCQ to study Mathematics (Maths) Class 12 for JEE Exam | Download free PDF with solutions
 1 Crore+ students have signed up on EduRev. Have you?
Test: Linear Programming (CBSE Level) - 2 - Question 1

### Let R be the feasible region (convex polygon) for a linear programming problem and let Z = ax + by be the objective function. When Z has an optimal value (maximum or minimum), where the variables x and y are subject to constraints described by linear inequalities,

Detailed Solution for Test: Linear Programming (CBSE Level) - 2 - Question 1

Let R be the feasible region (convex polygon) for a linear programming problem and let Z = ax + by be the objective function. When Z has an optimal value (maximum or minimum), where the variables x and y are subject to constraints described by linear inequalities,then , optimal value must occur at a corner point (vertex) of the feasible region.

Test: Linear Programming (CBSE Level) - 2 - Question 2

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

Detailed Solution for Test: Linear Programming (CBSE Level) - 2 - Question 2

Objective function is Z = 3x + 4 y ……(1).
The given constraints are : x + y ≤ 4, x ≥ 0, y ≥ 0.

therefore Z = 16 is maximum at ( 0 , 4 ) .

Test: Linear Programming (CBSE Level) - 2 - Question 3

### A factory manufactures two types of screws, A and B. Each type of screw requires the use of two machines, an automatic and a hand operated. It takes 4 minutes on the automatic and 6 minutes on hand operated machines tomanufacture a package of screws A, while it takes 6 minutes on automatic and 3 minutes on the hand operated machines to manufacture a package of screws B. Each machine is available for at the most 4 hours on any day. The manufacturer can sell a package of screws A at a profit of Rs 7 and screws B at a profit of Rs 10. Assuming that he can sell all the screws he manufactures, how many packages of each type should the factory owner produce in a day in order to maximize his profit? Determine the maximum profit.

Detailed Solution for Test: Linear Programming (CBSE Level) - 2 - Question 3

Let number of packages of screws A produced = x
And number of packages of screws B produced = y
Therefore , the above L.P.P. is given as :
Maximise , Z = 7x +10y , subject to the constraints : 4x +6y ≤ 240 and. 6x +3y ≤ 240 i.e. 2x +3y ≤ 120 and 2x +y ≤ 80 , x, y ≥ 0.

i.e 30 packages of screws A and 20 packages of screws B; Maximum profit = Rs 410.

Test: Linear Programming (CBSE Level) - 2 - Question 4

Determine the maximum value of Z = 11x + 7y subject to the constraints :2x + y ≤ 6, x ≤ 2, x ≥ 0, y ≥ 0.

Detailed Solution for Test: Linear Programming (CBSE Level) - 2 - Question 4

Here , maximize Z = 11x + 7y , subject to the constraints :2x + y ≤ 6, x ≤ 2, x ≥ 0, y ≥ 0.

Test: Linear Programming (CBSE Level) - 2 - Question 5

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

Detailed Solution for Test: Linear Programming (CBSE Level) - 2 - Question 5

Test: Linear Programming (CBSE Level) - 2 - Question 6

Let R be the feasible region for a linear programming problem, and let Z = ax + by be the objective function. If R is bounded, then

Detailed Solution for Test: Linear Programming (CBSE Level) - 2 - Question 6

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

Test: Linear Programming (CBSE Level) - 2 - Question 7

Minimise Z = – 3x + 4 y subject to x + 2y ≤ 8, 3x + 2y ≤ 12, x ≥ 0, y ≥ 0.

Detailed Solution for Test: Linear Programming (CBSE Level) - 2 - Question 7

Objective function is Z = - 3x + 4 y ……………………(1).
The given constraints are : x + 2y ≤ 8, 3x + 2y ≤ 12, x ≥ 0, y ≥ 0.

Here , Z = -12 is minimum at C (4 , 0) .

Test: Linear Programming (CBSE Level) - 2 - Question 8

A cottage industry manufactures pedestal lamps and wooden shades, each requiring the use of a grinding/cutting machine and a sprayer. It takes 2 hours on grinding/cutting machine and 3 hours on the sprayer to manufacture a pedestal lamp. It takes 1 hour on the grinding/cutting machine and 2 hours on the sprayer to manufacture a shade. On any day, the sprayer is available for at the most 20 hours and the grinding/cutting machine for at the most 12 hours. The profit from the sale of a lamp is Rs 5 and that from a shade is Rs 3. Assuming that the manufacturer can sell all the lamps and shades that he produces, how should he schedule his daily production in order to maximize his profit?

Detailed Solution for Test: Linear Programming (CBSE Level) - 2 - Question 8

Let number of pedestal lamps manufactured = x
And number of wooden shades manufactured = y
Therefore , the above L.P.P. is given as :
Maximise , Z = 5x +3y , subject to the constraints : 2x +y ≤ 12 and. 3x +2y ≤ 20 , x, y ≥ 0.

Here Z = 32 is maximum.
i.e 30 packages of screws A and 20 packages of screws B; Maximum profit = Rs 410.
i.e. 4 Pedestal lamps and 4 wooden shades; Maximum profit = Rs 32 .

Test: Linear Programming (CBSE Level) - 2 - Question 9

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

Detailed Solution for Test: Linear Programming (CBSE Level) - 2 - Question 9

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

Test: Linear Programming (CBSE Level) - 2 - Question 10

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

Detailed Solution for Test: Linear Programming (CBSE Level) - 2 - Question 10

Test: Linear Programming (CBSE Level) - 2 - Question 11

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

Detailed Solution for Test: Linear Programming (CBSE Level) - 2 - Question 11

Let R be the feasible region for a linear programming problem,and let Z = ax + by be the objective function. If R is bounded, then the objective function Z has both a maximum and a minimum value on R and each of these occurs at a corner point (vertex) of R.

Test: Linear Programming (CBSE Level) - 2 - Question 12

Minimize Z = 3x + 5y such that x + 3y ≥ 3, x + y ≥ 2, x, y ≥ 0.

Detailed Solution for Test: Linear Programming (CBSE Level) - 2 - Question 12

Objective function is Z = 3x + 5 y ……………………(1).
The given constraints are : x + 3y ≥ 3, x + y ≥ 2, x, y ≥ 0 .

Test: Linear Programming (CBSE Level) - 2 - Question 13

A company manufactures two types of novelty souvenirs made of plywood. Souvenirs of type A require 5 minutes each for cutting and 10 minutes each for assembling. Souvenirs of type B require 8 minutes each for cutting and 8 minutes each for assembling. There are 3 hours 20 minutes available for cutting and 4hours for assembling. The profit is Rs 5 each for type A and Rs 6 each for type B souvenirs. How many souvenirs of each type should the company manufacture in order to maximize the profit?

Detailed Solution for Test: Linear Programming (CBSE Level) - 2 - Question 13

Let number of souvenirs of type A = x
And number of souvenirs of type B = y
Therefore , the above L.P.P. is given as :
Maximise , Z = 5x +6y , subject to the constraints : 5x +8y ≤ 200 and. 10x +8y ≤ 240 , x, y ≥ 0.

Here Z = 160 is maximum.
i.e. 8 Souvenir of types A and 20 of Souvenir of type B; Maximum profit = Rs 160.

Test: Linear Programming (CBSE Level) - 2 - Question 14

Maximise the function Z = 11x + 7y, subject to the constraints: x ≤ 3, y ≤ 2,x ≥ 0, y ≥ 0.

Detailed Solution for Test: Linear Programming (CBSE Level) - 2 - Question 14

We have , Maximise the function Z = 11x + 7y, subject to the constraints: x ≤ 3, y ≤ 2,x ≥ 0, y ≥ 0.

Test: Linear Programming (CBSE Level) - 2 - Question 15

The feasible region for a LPP is shown in Figure. Evaluate Z = 4x + y at each of the corner points of this region. Find the minimum value of Z, if it exists

Detailed Solution for Test: Linear Programming (CBSE Level) - 2 - Question 15

Corner Points(4,0)(2,1)(0,3)​Corresponding value of Z 3 (Minimum)​

From the shaded region, it is clear that feasible region is unbounded with the corner points A(4, 0, B(2, 1) and C(0, 3).

Also, we have Z=4x+y ,

Now, we see that 3 is the smallest value of Z at the corner point (0, 3). Note that here we see that the region is unbounded, therefore 3 may or may not be the minimum value of Z.

To decide this issue, we graph the inequality 4x+y<3 and check whether the resulting open half plan has no point in common with feasible region otherwise, Z has no minimum value.

From the shown graph above, it is clear that there is no point in common with feasible region and hence Z is minimum value of 3 at (0, 3).

Test: Linear Programming (CBSE Level) - 2 - Question 16

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

Detailed Solution for Test: Linear Programming (CBSE Level) - 2 - Question 16

A maximum or a minimum may not exist for a linear programming problem if The feasible region is unbounded .

Test: Linear Programming (CBSE Level) - 2 - Question 17

Maximize Z = 3x + 2y subject to x + 2y ≤ 10, 3x + y ≤ 15, x, y ≥ 0.

Detailed Solution for Test: Linear Programming (CBSE Level) - 2 - Question 17

Objective function is Z = 3x + 2 y ……………………(1).
The given constraints are : x + 2y ≤ 10, 3x + y ≤ 15, x, y ≥ 0.

Test: Linear Programming (CBSE Level) - 2 - Question 18

A merchant plans to sell two types of personal computers – a desktop model and a portable model that will cost Rs 25000 and Rs 40000 respectively. He estimates that the total monthly demand of computers will not exceed 250 units. Determine the number of units of each type of computers which the merchant should stock to get maximum profit if he does not want to invest more than Rs 70 lakhs and if his profit on the desktop model is Rs 4500 and on portable model is Rs 5000.

Detailed Solution for Test: Linear Programming (CBSE Level) - 2 - Question 18

Let number of desktop model computers = x
And number of portable model computers = y
Therefore , the above L.P.P. is given as :
Maximise , Z = 4500x +5000y , subject to the constraints : x +y ≤ 250 and 25000x +40000y ≤ 700000 .i.e. x +y ≤ 250 and 5x +8y ≤ 1400 , x, y ≥ 0.

Here Z = 1150000 is maximum.
i.e. 200 units of desktop model and 50 units of portable model; Maximum profit = Rs 1150000 .

Test: Linear Programming (CBSE Level) - 2 - Question 19

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

Detailed Solution for Test: Linear Programming (CBSE Level) - 2 - Question 19

Test: Linear Programming (CBSE Level) - 2 - Question 20

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

Detailed Solution for Test: Linear Programming (CBSE Level) - 2 - Question 20

Test: Linear Programming (CBSE Level) - 2 - Question 21

In Corner point method for solving a linear programming problem the first step is to

Detailed Solution for Test: Linear Programming (CBSE Level) - 2 - Question 21

In Corner point method for solving a linear programming problem the first step is : To find the feasible region of the linear programming problem and determine its corner points (vertices)

Test: Linear Programming (CBSE Level) - 2 - Question 22

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

Detailed Solution for Test: Linear Programming (CBSE Level) - 2 - Question 22

Objective function is Z = x + 2y ……………………(1).
The given constraints are : 2x + y ≥ 3, x + 2y ≥ 6, x, y ≥ 0 .

Here , Z = 18 is minimum at (0, 3) and (6 , 0) .
Minimum Z = 6 at all the points on the line segment joining the points (6, 0) and (0, 3).

Test: Linear Programming (CBSE Level) - 2 - Question 23

A diet is to contain at least 80 units of vitamin A and 100 units of minerals. Two foods F1 and F2 are available. Food F1 costs Rs 4 per unit food and F2 costs Rs 6 per unit. One unit of food F1 contains 3 units of vitamin A and 4 units of minerals. One unit of food F2 contains 6 units of vitamin A and 3 units of minerals. Formulate this as a linear programming problem. Find the minimum cost for diet that consists of mixture of these two foods and also meets the minimal nutritional requirements.

Detailed Solution for Test: Linear Programming (CBSE Level) - 2 - Question 23

Let number of units of food F1 = x
And number of units of food F2 = y
Therefore , the above L.P.P. is given as :
Minimise , Z = 4x +6y , subject to the constraints : 3 x + 6y ≥ 80, 4x + 3y ≥ 100, x,y ≥ 0.

Corner points Z =4x +6 y B(80/3 , 0) 320/3 D(24,4/3 ) 104…………………(Min.) A(0,100/3) 200 Here Z = 104 is minimum. i.e. Minimum cost = Rs 104.

Test: Linear Programming (CBSE Level) - 2 - Question 24

Maximize Z = 100x + 120y , subject to constraints 2x + 3y ≤ 30, 3x + y ≤ 17, x ≥ 0, y ≥ 0.

Detailed Solution for Test: Linear Programming (CBSE Level) - 2 - Question 24

We have , Maximize Z = 100x + 120y , subject to constraints 2x + 3y ≤ 30, 3x + y ≤ 17, x ≥ 0, y ≥ 0.

Test: Linear Programming (CBSE Level) - 2 - Question 25

Determine the minimum value of Z = 3x + 4y if the feasible region (shaded) for a LPP is shown in Figure above.

## Mathematics (Maths) Class 12

204 videos|288 docs|139 tests
Information about Test: Linear Programming (CBSE Level) - 2 Page
In this test you can find the Exam questions for Test: Linear Programming (CBSE Level) - 2 solved & explained in the simplest way possible. Besides giving Questions and answers for Test: Linear Programming (CBSE Level) - 2, EduRev gives you an ample number of Online tests for practice

## Mathematics (Maths) Class 12

204 videos|288 docs|139 tests