Question 1 :
A vertex of the linear inequalities {tex} 2 x + 3 y \leq 6 ,\ x + 4 y \leq 4 {/tex} and {tex} x , y \geq 0 , {/tex} is

Question 2 :
The constraints<br> {tex} \quad - x _ { 1 } + x _ { 2 } \leq 1 {/tex}<br> {tex}\quad - x _ { 1 } + 3 x _ { 2 } \leq 9 {/tex} <br>{tex}\ \ \ \quad x _ { 1 } , x _ { 2 } \geq 0 {/tex} <br>define on<br><img style='object-fit:contain' src="https://storage.googleapis.com/teachmint/question_assets/JEE%20Main/5dd68253f197791516a5f254"><br>

Question 3 :
If he purchases the number of articles of {tex} A {/tex} and {tex} B ,\ x {/tex} and {tex} y {/tex} respectively, then linear constraints are

Question 4 :
If the products made {tex}x{/tex} of {tex}A{/tex} and {tex}y{/tex} of {tex}B{/tex}, then the linear constraints for the LP.P. except {tex}x \geq 0, \ y\geq0{/tex}, are

Question 5 :
The minimum value of the objective function {tex} z = 2 x + 10 y {/tex} for linear constraints {tex} x \geq 0 ,\ y \geq 0 {/tex}, {tex} x - y \geq 0 ,\ x - 5 y \leq - 5 {/tex}, is

Question 6 :
For the L.P. problem {tex} { Max }\ z = 3 x + 2 y {/tex} subject to {tex} x + y \geq 1 , \ y - 5 x \leq 0 , \ x - y \geq - 1 , \ x + y \leq 6 , \ x \leq 3 {/tex} and {tex} x , y \geq 0 {/tex}

Question 7 :
The maximum value of {tex} z = 4 x + 3 y {/tex} subject to the constraints {tex} 3 x + 2 y \geq 160, \ 5x + 2 y \geq 200 ,\ x + 2 y \geq 80 {/tex}; {tex} x ,\ y \geq 0 {/tex} is

Question 8 :
By graphical method, the solution of linear programming problem <br>Maximize {tex} z = 3 x _ { 1 } + 5 x _ { 2 } {/tex} <br>Subject to {tex} 3 x _ { 1 } + 2 x _ { 2 } \leq 18 , \ x _ { 1 } \leq 4 , \ x _ { 2 } \leq 6 ,\ x _ { 1 } \geq 0 {/tex}, {tex} x _ { 2 } \geq 0 {/tex} is

Question 9 :
The objective function {tex} z = 4 x + 3 y {/tex} can be maximized subjected to the constraints {tex} 3 x + 4 y \leq 24,\ 8 x + 6 y \leq 48 {/tex}, {tex} x \leq 5 ,\ y \leq 6 ; \ x , y \geq 0 {/tex}

Question 10 :
If {tex} 3 x _ { 1 } + 5 x _ { 2 } \leq 15,\ 5 x _ { 1 } + 2 x _ { 2 } \leq 10 ,\ x _ { 1 } ,\ x _ { 2 } \geq 0 {/tex} then the maximum value of {tex} 5 x _ { 1 } + 3 x _ { 2 } , {/tex} by graphical method is

Question 11 :
The true statement for the graph of inequations {tex} 3 x + 2 y \leq 6 {/tex} and {tex} 6 x + 4 y \geq 20 {/tex}, is

Question 12 :
The maximum value of {tex} z = 5 x + 2 y , {/tex} subject to the constraints {tex} x + y \leq 7 ,\ x + 2 y \leq 10 ,\ x ,\ y \geq 0 {/tex} is

Question 13 :
To maximize the objective function {tex} z = 2 x + 3 y {/tex} under the constraints {tex} x + y \leq 30 ,\ x - y \geq 0 ,\ y \leq 12 , \ x \leq 20 , \ y \geq 3 {/tex} and {tex} x , y \geq 0 {/tex}

Question 14 :
The maximum value of objective function {tex} c = 2 x + 3 y {/tex} in the given feasible region, is<br><img style='object-fit:contain' src="https://data-screenshots.sgp1.digitaloceanspaces.com/5dd651a345e5857e55665667.jpg" />

Question 15 :
The points which provides the solution to the linear programming problem: {tex} { Max }\ ( 2 x + 3 y ) {/tex} subject to constraints: {tex} x \geq 0 ,\ y \geq 0,\ 2 x + 2 y \leq 9,\ 2 x + y \leq 7 {/tex}, {tex} x + 2 y \leq 8 {/tex}, is

Question 16 :
The maximum value of {tex} P = x + 3 y {/tex} such that {tex} 2 x + y \leq 20 {/tex}, {tex} x + 2 y \leq 20 ,\ x \geq 0 ,\ y \geq 0 , {/tex} is

Question 17 :
Minimize {tex} z = \sum \limits _ { j = 1 } ^ { n } \sum \limits_ { i = 1 } ^ { m } c _ { i j } x _ { i j } {/tex} <br>Subject to: {tex} \sum \limits _ { j = 1 } ^ { n } x _ { i j } \leq a _ { i } , i = 1 , \ldots \ldots m {/tex} <br>{tex}\quad \quad \quad \quad \sum \limits _ { i = 1 } ^ { m } x _ { i j } = b _ { j } , j = 1 , \ldots \ldots n {/tex} <br>is a (LPP) with number of constraints

Question 18 :
A company manufactures two types of products {tex} A {/tex} and {tex} B {/tex}. The storage capacity of its godown is 100 units. Total investment amount is Rs. 30,000. The cost price of {tex} A {/tex} and {tex} B {/tex} are Rs. 400 and Rs. 900 respectively. If all the products have sold and per unit profit is Rs. 100 and Rs. 120 through {tex} A {/tex} and {tex} B {/tex} respectively. If {tex} x {/tex} units of {tex} A {/tex} and {tex} y {/tex} units of {tex} B {/tex} be produced, then two linear constraints and iso-profit line are respectively

Question 19 :
A company manufactures two types of telephone sets {tex} A {/tex} and {tex} B {/tex}. The {tex} A {/tex} type telephone set requires 2 hour and {tex} B {/tex} type telephone requires 4 hour to make. The company has 800 work hour per day. 300 telephone can pack in a day. The selling prices of {tex} A {/tex} and {tex} B {/tex} type telephones are Rs. 300 and 400 respectively. For maximum profits company produces {tex} x {/tex} telephones of {tex} A {/tex} type and {tex} y {/tex} telephones of {tex} B {/tex} types. Then except {tex} x \geq 0 {/tex} and {tex} y \geq 0 {/tex}, linear constraints and the probable region of the L.P.P is of the type

Question 20 :
The vertices of a feasible region of the above question are

Question 21 :
For the L.P. problem {tex} \operatorname { Min } z = 2 x _ { 1 } + 3 x _ { 2 } {/tex} such that {tex} - x _ { 1 } + 2 x _ { 2 } \leq 4 , \quad x _ { 1 } + x _ { 2 } \leq 6 ,\ x _ { 1 } + 3 x _ { 2 } \geq 9 {/tex} and {tex} x _ { 1 } ,\ x _ { 2 } \geq 0 {/tex}

Question 22 :
For the constraints of a L.P. problem given by {tex} x _ { 1 } + 2 x _ { 2 } \leq 2000 , x _ { 1 } + x _ { 2 } \leq 1500 , x _ { 2 } \leq 600 {/tex} and {tex} x _ { 1 } , x _ { 2 } \geq 0 {/tex} which one of the following points does not lie in the positive bounded region

Question 23 :
For the following linear programming problem : minimize {tex} z = 4 x + 6 y {/tex} subject to the constraints {tex} 2 x + 3 y \geq 6 {/tex}, {tex} x + y \leq 8 ,\ y \geq 1 ,\ x \geq 0 {/tex}, the solution is

Question 24 :
A factory produces two products {tex} A {/tex} and {tex} B {/tex}. In the manufacturing of product {tex} A {/tex}, the machine and the carpenter requires 3 hour each and in manufacturing of product {tex} B {/tex}, the machine and carpenter requires 5 hour and 3 hour respectively. The machine and carpenter work profit on {tex} A {/tex} and {tex} B {/tex} is Rs. 6 and 8 respectively. If profit is maximum by manufacturing {tex} x {/tex} and {tex} y {/tex} units of {tex} A {/tex} and {tex} B {/tex} type product respectively, then for the function {tex} 6 x + 8 y {/tex} the constraints are

Question 25 :
The minimum value of {tex} z = 2 x _ { 1 } + 3 x _ { 2 } {/tex} subject to the constraints {tex} 2 x _ { 1 } + 7 x _ { 2 } \geq 22 ,\ x _ { 1 } + x _ { 2 } \geq 6,\ 5 x _ { 1 } + x _ { 2 } \geq 10 {/tex} and {tex} x _ { 1 } ,\ x _ { 2 } \geq 0 {/tex} is

Question 26 :
The maximum value of {tex} z = 3 x + 4 y {/tex} subject to the constraints {tex} x + y \leq 40 ,\ x + 2 y \leq 60 ,\ x \geq 0 {/tex} and {tex} y \geq 0 {/tex} is

Question 27 :
Mohan wants to invest the total amount of Rs.15,000 in saving certificates and national saving bonds. According to rules, he has to invest at least Rs. 2000 in saving certificates and Rs. 2500 in national saving bonds. The interest rate is 8{tex}\% {/tex} on saving certificate and 10{tex} \% {/tex} on national saving bonds per annum. He invest Rs. {tex} x {/tex} in saving certificates and Rs. {tex} y{/tex} in national saving bonds. Then the objective function for this problem is

Question 28 :
For the L.P. problem {tex} { Min }\ z = x _ { 1 } + x _ { 2 } {/tex} such that {tex} 5 x _ { 1 } + 10 x _ { 2 } \leq 0 ,\ x _ { 1 } + x _ { 2 } \geq 1 ,\ x _ { 2 } \leq 4 {/tex} and {tex} x _ { 1 } ,\ x _ { 2 } \geq 0 {/tex}

Question 29 :
For the following feasible region, the linear constraints except {tex} x \geq 0 {/tex} and {tex} y \geq 0 , {/tex} are<br><img style='object-fit:contain' src="https://data-screenshots.sgp1.digitaloceanspaces.com/5dd6512a45e5857e55665666.jpg" />

Question 30 :
The maximum value of {tex} P = 6 x + 8 y {/tex} subject to constraints {tex} 2 x + y \leq 30 ,\ x + 2 y \leq 24 {/tex} and {tex} x \geq 0 ,\ y \geq 0 {/tex} is

Question 31 :
Two tailors {tex} A {/tex} and {tex} B {/tex} earns Rs. 15 and Rs. 20 per day respectively. {tex} A {/tex} can make 6 shirts and 4 pants in a day while {tex} B {/tex} can make 10 shirts and 3 pants. To spend minimum on 60 shirts and 40 pants, {tex} A {/tex} and {tex} B {/tex} working {tex} x {/tex} and {tex} y {/tex} days respectively. Then linear constraints except {tex} x \geq 0 ,\ y \geq 0 , {/tex} are and objective function are respectively

Question 32 :
The solution of set of constraints {tex} x + 2 y \geq 11 {/tex}, {tex} 3 x + 4 y \leq 30,\ 2 x + 5 y \leq 30 ,\ x \geq 0 ,\ y \geq 0 {/tex} includes the point

Question 33 :
A wholesale merchant wants to start the business of cereal with Rs. 24000. Wheat is Rs. 400 per quintal and rice is Rs. 600 per quintal. He has capacity to store 200 quintal cereal. He earns the profit Rs. 25 per quintal on wheat and Rs. 40 per quintal on rice. If he stores {tex} x {/tex} quintal rice and {tex} y {/tex} quintal wheat, then for maximum profit the objective function is

Question 34 :
For the following shaded area, the linear constraints except {tex} x \geq 0 {/tex} and {tex} y \geq 0 {/tex}, are<br><img style='object-fit:contain' src="https://storage.googleapis.com/teachmint/question_assets/JEE%20Main/5dd62b8624b7e6689423479b">

Question 35 :
The maximum value of {tex} 4 x + 5 y {/tex} subject to the constraints {tex} x + y \leq 20 ,\ x + 2 y \leq 35 ,\ x - 3 y \leq 12 {/tex} is

Question 36 :
The point at which the maximum value of {tex} ( x + y ) , {/tex} subject to the constraints {tex} x + 2 y \leq 70,\ 2 x + y \leq 95 , \ x ,\ y \geq 0 {/tex} is obtained, is

Question 37 :
The maximum value of {tex} ( x + 2 y ) {/tex} under the constraints {tex} 2 x + 3 y \leq 6 ,\ x + 4 y \leq 4 ,\ x ,\ y \geq 0 {/tex} is