11th Standard Syllabus & Materials
11th Standard
TN 11th Tamil இயற்கை வேளாண்மை,சுற்றுச்சூழல் -செய்யுள் - மனோன்மணீயம் Important Questions And Answers Study Material - QB365 Set A
NEW11th Standard
TN 11th Tamil என்னுயிர் என்பேன் -துணைப்பாடம் - இசைத்தமிழர் இருவர் Important Questions And Answers Study Material - QB365 Set A
NEW11th Standard
TN 11th Tamil மொழி கலை -செய்யுள் - ஒவ்வொரு புல்லையும் Important Questions And Answers Study Material - QB365 Set A
NEW11th Standard
TN 11th Tamil பீடு பெற நில் - இலக்கணம் - பகுபத உறுப்புகள் Important Questions And Answers Study Material - QB365 Set A
NEW11th Standard
TN 11th Tamil பீடு பெற நில் - துணைப்பாடம் - வாடிவாசல் Important Questions And Answers Study Material - QB365 Set A
NEW11th Standard
TN 11th Tamil பீடு பெற நில் - செய்யுள் - குறுந்தொகை Important Questions And Answers Study Material - QB365 Set A
Published on: 13/05/2022
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Creative Questions in class 11 Business Maths Subject.It will helps to get more idea about question pattern in every Creative questions with solution.
Download Tamil Nadu 11th Standard Business Maths and Statistics question papers, model tests, one-mark questions, important questions, and public exam papers in PDF format. Free study materials and answer keys for TN State Board students.
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Take MCQ Business Maths and Statistics Test
1.
Every gram of wheat provides 0.1 g of proteins and 0.25 g of carbohydrates. The corresponding values of rice are 0.05 g and 0.5 g respectively. Wheat cost Rs.4 per kg and rice cost Rs.6 per kg. The minimum daily requirements of proteins and carbohydrate for an average child are 50 g and 200 g respectively. In what quantities should wheat and rice be mixed in the daily diet to provide minimum daily requirements of proteins and carbohydrate at minimum cost. Frame an LPP and solve it graphically.
2.
A manufacturer makes two types of toys A and B. Three machines are needed for this purpose and the time (min) required for each toy on the machine is given below:
| Type | Machine I | Machine II | Machine III |
| A | 12 | 18 | 6 |
| B | 6 | 0 | 9 |
Each machine is available for a maximum of 6 hours/day. If the profit on each toy of type A is Rs.7.50 and for B is Rs.5. Show that 15 toys of type A and 30 of type B should be manufactured in a day to get maximum profit.
3.
One kind of the cake requires 200 g of flour and 25 g of fat, and another kind of cake requires 100 g of flour and 50 g of fat. Find the maximum number of cakes which can be made from 5 kg of flour and 1 kg of fat assuming that there is no shortage of other ingredients used in making the cakes?
4.
Reshma wishes to mix two types of food P and Q in such a way that the Vitamin contents of the mixture contain at least 8 units of vitamin A and 11 units of vitamin B. Food P costs Rs.60/kg and Food Q costs Rs.80/kg. Food P contains 3 units 1 kg of vitamin A and 5 units 1 kg of vitamin B while food Q contains 4 units 1 kg of vitamin A and 2 units 1 kg of vitamin B. Determine the minimum cost of the mixture.
5.
A manufacturer produces two types of steel trunks. He has two machine A and B. For completing, the first type of the trunk requires 3 hours on machine A and 2 hours on machine B, whereas the second type of the trunk requires 3 hours on machine A and 3 hours on machine B. Machines A and B can work at the most for 18 hours and 14 hours per day respectively. He earns a profit of Rs.30 andRs.40 per trunk of the first type and second type respectively. How many trunks of the each type must he make each day to make maximum profit?
1.
Let x1 g of wheat and x2 g of rice be mixed in the daily diet. Let Z be the minimum cost of diet.
| Proteins | Carbohydrates | Cost | |
|---|---|---|---|
| 1 g of Wheat | 0.1 g | 0.25 g | Rs.4/kg |
| 1 g of Rice | 0.05 g | 0.5 g | Rs.6/kg |
| Minimum Requirement |
50 g | 200 g |
Thus, the mathematical formulation of the LPP
Minimize \(Z=\frac { 4{ x }_{ 1 } }{ 1000 } +\frac { 6{ x }_{ 2 } }{ 1000 } \quad \Rightarrow \quad Z=\frac { { x }_{ 1 } }{ 250 } +\frac { 3{ x }_{ 2 } }{ 500 } \)
Subject to the constraints
\(0.1{ x }_{ 1 }+0.05{ x }_{ 2}\ge 50 \Rightarrow 2{ x }_{ 1 }+{ x }_{ 2 }\ge 1000\)
\( 0.25{ x }_{ 1 }+0.5{ x }_{ 2\quad }\ge 200 \Rightarrow { x }_{ 1 }+2{ x }_{ 2 }\ge 800\)
\(and\ { x }_{ 1 },{ x }_{ 2 }\ge 0\)
Consider the equation
\(2{ x }_{ 1 }+{ x }_{ 2 }= 1000\)
| \({ x }_{ 1 }\) | 0 | 500 |
| \({ x }_{ 2 }\) | 1000 | 0 |
\({ x }_{ 1 }+2{ x }_{ 2 }= 800\)
| \({ x }_{ 1 }\) | 0 | 500 |
| \({ x }_{ 2 }\) | 1000 | 0 |
The feasible region is ABC an its co-ordinates are A(800, 0), C(0, 1000) and B is the point of intersection of the lines 2x1+ x2 = 1000 ... (1) x1+ 2x2 = 800 ... (2)
Verification of B:
\(\Rightarrow (1)\times 2 4{ x }_{ 1 }+2{ x }_{ 2 }=2000\)
\(\quad (-)\quad (-)\quad \quad (-)\)
\(\Rightarrow (2) 15{ x }_{ 1 }+6{ x }_{ 2 }=30 \Rightarrow { x }_{ 1 }=400\)
\(--------------\)
Substracting, \(3{ x }_{ 1 }=2000\)
From (2), \(\quad 400+2{ x }_{ 2 }=800\)
\(2{ x }_{ 2 }=400\quad \Rightarrow \quad { x }_{ 2 }=200\)
| Corner Points | \( Z=\frac { { x }_{ 1 } }{ 250 } +\frac { 3{ x }_{ 2 } }{ 500 } \) |
|---|---|
| A(800,0) | \(\frac { 800 }{ 250 } =3.2\) |
| B(400, 200) | \(\frac { 400 }{ 250 } +\frac { 600 }{ 500 } =2.8\) |
| C(0,1000) | \(\frac { 3000 }{ 500 } =6\) |
Minimum of Z occurs at B(400, 200). Hence, the solution is x1= 400, x2 = 200 and Zrnin = 2.8
2.
Let x1 toys of type A and x2 toys of type B are produced. Let Z be the maximum profit on two types of toys A and B.
| Type | Machine I | Machine II | Machine III | Profit |
|---|---|---|---|---|
| A | 12 | 18 | 6 | Rs. 7.50 |
| B | 6 | 0 | 9 | Rs. 5 |
| Time available | 6h = 360 min | 6h = 360 min | 6h = 360 min |
Thus, the mathematical formulation of the LPP is maximize Z = 7.50x1 + 5x2
Subject to the constraints
12x1 + 6x2 ≤ 360,18x1 ≤ 360,6x1 + 9x2 ≤ 360,x1,x2 ≥ 0
Consider the equations
12x1 + 6x2 ≤ 360
| \({ x }_{ 1 }\) | 0 | 30 |
| \({ x }_{ 2 }\) | 60 | 0 |
\(18{ x }_{ 1 }=360\)
| x1 | 20 |
\({ 6x }_{ 1 }+9{ x }_{ 2 }=360\)
| \({ x }_{ 1 }\) | 0 | 60 |
| \({ x }_{ 2 }\) | 40 | 0 |
X1 = 20 is a line parallel to x2-axis at a distance of 20 units from it
The feasible region is OABCD and its co-ordinates are O(0, 0) A(20, 0) D(0, 40), B is the point of intersection ofthe lines x1 = 20 and 12x1+ 6x2 = 360
\(\Rightarrow 2{ x }_{ 1 }+{ x }_{ 2 }=60\)
\(\Rightarrow 40+{ x }_{ 2 }=60\)
\( \Rightarrow { x }_{ 2 }=20\)
Verification of Band C:
\(\therefore \quad B\quad (20,20)\)
And C is the point of intersection of the lines
\(2{ x }_{ 1 }+{ x }_{ 2 }=60...(1)\)
\( (-)\quad \quad (-)\quad \quad (-)\)
\(2{ x }_{ 1 }+3{ x }_{ 2 }=120 \left[ \because \quad 6{ x }_{ 1 }+{ 9x }_{ 2 }=360 \right] ...(2)\)
\(-------------\)
\( -2x_{ 2 }=-60 \Rightarrow { x }_{ 2 }=30\)
\(2{ x }_{ 1 }+30=60 [\because \quad From\quad (1)] \Rightarrow { x }_{ 1 }=\frac { 30 }{ 2 } =15\)
\( \therefore \quad C\quad is\quad (15,30)\)
| Corner Points | Z = 7.5x1 + 5x2 |
|---|---|
| O(0,0) | 0 |
| A(20,0) | 150 |
| B(20, 20) | 250 |
| C(15,30) | 262.5 |
| D(0, 40) | 200 |
Maximum of Z occurs at (15,30)
Hence, the solution is x1 = 15, x2 = 30 and Zmax= 262.5
3.
Let x1cakes of the one kind and x2 cakes of another kind are made. Let Z be the maximum number of cakes
| Ingredients | x1(g) | x2(g) | Total (kg) |
| Flour | 200 | 100 | 5 |
| Fat | 25 | 50 | 1 |
Thus, the mathematical formulation of the LPP is Maximize Z = x1+ x2
Subject to the constraints
\(200{ x }_{ 1 }+100{ x }_{ 2 }\le 5000\)
\(25{ x }_{ 1 }+50{ x }_{ 2 } \le 1000\)
\({ x }_{ 1 },{ x }_{ 2 }\ge 0\)
Consider the equations
\(200{ x }_{ 1 }+100{ x }_{ 2 }= 5000\)
| \({ x }_{ 1 }\) | 0 | 25 |
| \({ x }_{ 2 }\) | 50 | 0 |
\(25{ x }_{ 1 }+50{ x }_{ 2 }=1000\)
| \({ x }_{ 1 }\) | 0 | 25 |
| \({ x }_{ 2 }\) | 50 | 0 |
The feasible region is OABC and its co-ordinates are O(0, 0) A(25, 0) C(O, 20) and B is the point of intersection of the lines
200x1 + 100x2 = 1000 .... (1)
and 25x1 + 50x2 = 1000 ... (2)
Verification of B:
\((1) \Rightarrow 200{ x }_{ 1 }+100{ x }_{ 2 }=5000\)
\( (-)\quad \quad \quad (-)\quad \quad (-)\)
\( (2)\times 5\Rightarrow 50{ x }_{ 1 }+100{ x }_{ 2 }=2000\)
\(------------------\)
\(150x_{ 1 }=3000 \Rightarrow { x }_{ 1 }=20\)
\(From(2), 25(20)+50{ x }_{ 2 }=1000\Rightarrow 500+50{ x }_{ 2 }=1000 \Rightarrow 50{ x }_{ 2 }=500\)
\(\Rightarrow { x }_{ 2 }=10\)
\(\therefore B\ is\ (20,10)\)
| Corner Points | Z=x1 +x2 |
|---|---|
| O(0,0) | 0 |
| A(25, 0) | 25 |
| B(20, 10) | 30 |
| C(0,20) | 20 |
Maximum of Z occurs at B(20, 10)
Hence, the solution is x1 = 20, x2 = 10 and Zmax = 30.
4.
Let Reshma mix x1 kg of food P and x2 kg of food Q to make the mixture.
Let Z be the total cost of mixture
| Food P | Food Q | Minimum requirement | |
|---|---|---|---|
| Vitamin A | 3 | 4 | 8 |
| Vitamin B | 5 | 2 | 11 |
| Cost | Rs.60 | Rs.80 |
Thus, the mathematical formation of the given LPP is minimize Z = 60x1+ 80x2
Subject to the constraints
\(3{ x }_{ 1 }+4{ x }_{ 2 }\ge 8\quad 5{ x }_{ 1 }+2{ x }_{ 2 }\ge 11\quad and\quad { x }_{ 1 },{ x }_{ 2 }\ge 0\)
Consider the equations
\(3{ x }_{ 1 }+4{ x }_{ 2 }=8\)
| \({ x }_{ 1 }\) | 0 | 8/3 |
| \({ x }_{ 2 }\) | 2 | 0 |
\(5{ x }_{ 1 }+2{ x }_{ 2 }=11\)
| \({ x }_{ 1 }\) | 0 | 8/3 |
| \({ x }_{ 2 }\) | 2 | 0 |
The feasible region is ABC and its co-ordinates are A\(\left( \frac { 8 }{ 3 } ,0 \right) \), C\(\left( 0,\ \frac { \pi }{ 2 } \right) \)and B is the point of intersection of the lines 3x1 + 4x2 = 8 ..... (1) and 5x1 + 2x2 = 11 .... (2)
Verification of B:
\((1) \Rightarrow 3{ x }_{ 1 }+4{ x }_{ 2 }=8\)
\( (-)\quad (-)\quad \quad (-)\)
\((2)\times 2\Rightarrow 10{ x }_{ 1 }+4{ x }_{ 2 }=22\)
\(--------------\)
\( -7x_{ 1 }=-14 \Rightarrow { x }_{ 1 }=2\)
\(From(1), 3(2)+4{ x }_{ 2 }=8\)
\(4{ x }_{ 2 }=8-6=2\Rightarrow { x }_{ 2 }=\frac { 1 }{ 2 } \)
\( \therefore \ B\ is\ \left( 2,\frac { 1 }{ 2 } \right) \)
| Corner Points | Z = 60x1+ 80x2 |
|---|---|
| A(8/3,0) | \(60\times \frac { 8 }{ 3 } =160\) |
| B (2, 1/2) | \(120+80\times \frac { 1 }{ 2 } =160\) |
| C(0,11/2) | \(80\times \frac { 11 }{ 2 } =440\) |
Minimum of Z occurs at \(A\left( \frac { 8 }{ 3 } ,0 \right) and\quad B\left( 2,\frac { 1 }{ 2 } \right) \)
Hence, least cost of mixture is n60 when 8/3 kg of food P and 0 kg of food Q and 2 kg of food P and 112kg of food Q are mixed
5.
Let the manufacturer produce x1 trunks of first type and x2 trunks of second type each day.
Let Z be the total profit of the manufacturer.
| Trunk of I Type (hrs) | Trunk of II Type (hrs) | Maximum time available (hrs) | |
|---|---|---|---|
| Machine A | 3 | 3 | 18 |
| Machine B | 2 | 3 | 14 |
| Profit | Rs.30 | Rs.40 |
Thus, the mathematical formulation of the LPP is maximize Z = 30x1+ 40x2
Subject to the constraints
3x1 + 3x2 ≤ 18,2x1 + 3x2 ≤ 14 and x1 + x2 ≥ 0
Consider the equations
\(3{ x }_{ 1 }+3{ x }_{ 2 }= 18\)
| \({ x }_{ 1 }\) | 0 | 6 |
| \({ x }_{2 }\) | 6 | 0 |
\(2{ x }_{ 1 }+3{ x }_{ 2 }=14\)
| \({ x }_{ 1 }\) | 0 | 7 |
| \({ x }_{2 }\) | 14/3 | 0 |
The feasible region is OABC and its co-ordinates are O(0, 0), A(6, 0), c(0, 14/3) and B is the point of intersection of 3x1 + 3x2 = 18 and 2x1 + 3x2 = 14
Verification of B:
\(3{ x }_{ 1 }+3{ x }_{ 2 }=18 ...(1)\)
\( (-)\quad (-)\quad \quad (-)\)
\(2{ x }_{ 1 }+3{ x }_{ 2 }=14...(2)\)
\(-------------\)
x1 = 4
From 2x1 + 3x2 = 14, we get 8 + 3x2 = 14 ⇒ 3x2 = 6 ⇒ x2 = 2
\(\therefore \text {B is} (4,2)\)
| Corner Points | Z=30x1+40x2 |
|---|---|
| O(0,0) | 0 |
| A(6,0) | 180 |
| B (4, 2) | 200 |
| C(0, 14/3) | 40(14/3) = 560/3 |
Maximum of Z occurs at B( 4, 2)
Hence, the solution is x1 = 4, x2 = 2 and Zmax = 200.
11th Standard Syllabus & Materials
11th Standard
TN 11th Tamil பீடு பெற நில் - செய்யுள் - காவடிச்சிந்து Important Questions And Answers Study Material - QB365 Set A
NEW11th Standard
TN 11th Tamil பீடு பெற நில் - உரைநடை - மலை இடப்பெயர்கள் : ஓர் ஆய்வு Important Questions And Answers Study Material - QB365 Set A
NEW11th Standard
TN 11th Tamil மாமழை போற்றுதும் - துணைப்பாடம் - யானை டாக்டர் Important Questions And Answers Study Material - QB365 Set A
NEW11th Standard
TN 11th Tamil மாமழை போற்றுதும் - செய்யுள் - ஐங்குறுநூறு Important Questions And Answers Study Material - QB365 Set A
Tamilnadu Stateboard 11th Standard Subjects
Maths
Commerce
Economics
Biology
Business Maths and Statistics
Accountancy
Computer Science
Physics
Chemistry
Maths
Biology
Economics
Physics
Chemistry
History
Business Maths and Statistics
Computer Science
Accountancy
Computer Applications
History
Computer Technology
Commerce
Computer Applications
Computer Technology
Tamil
English
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Tamilnadu Stateboard Standards
