Cutting alternatives | Width of Rolls(cm) 3 | Width of Rolls(cm) 4 | Width of Rolls(cm) 6 | Width of Rolls(cm) 10 | Waste(cm) |
1 | 4 | 3 | - | - | - |
2 | - | 3 | 2 | - | - |
3 | 1 | 1 | 1 | 1 | 1 |
4 | - | - | 2 | 1 | 2 |
5 | - | 4 | 1 | - | 2 |
6 | 3 | 2 | 1 | - | 1 |
Roll width(cm) | Demand |
2 | 2,000 |
4 | 3,600 |
6 | 1,600 |
10 | 500 |
Vitamin A | Vitamin B | Vitamin C | |
Food X | 1 | 2 | 3 |
Food Y | 2 | 2 | 1 |
Items | Number of hours required on machines | ||
I | II | III | |
M | 1 | 2 | 1 |
N | 2 | 1 | 1.25 |
Types of Toys | Machines | Machines | Machines |
I | II | III | |
A | 12 | 18 | 6 |
B | 6 | 0 | 9 |
Transportation cost per quintal (in Rs) | ||
From/ To | A | B |
D | 6 | 4 |
E | 3 | 2 |
F | 2.50 | 3 |
Food | Vitamin A | Vitamin B | Vitamin C |
X | 1 | 2 | 3 |
Y | 2 | 2 | 1 |
Distance in (km.) | ||
From/ To | A | B |
D | 7 | 3 |
E | 6 | 4 |
F | 3 | 2 |
Kg per bag | ||
Brand P | Brand Q | |
Nitrogen | 3 | 3.5 |
Phosphoric acid | 1 | 2 |
Potash | 3 | 1.5 |
Chlorine | 1.5 | 2 |
Ingredient | Brand Y Feed | Brand Z Feed | Minimum Monthly Requirement |
A | 5 oz | 10 oz | 90 oz |
B | 4 oz | 3 oz | 48 oz |
C | .5 oz | 0 | 1.5 oz |
Cost/lb | $0.2 | $.03 |
Branch Manager | Monthly Business (Rs. lakh) | |||
A | B | C | D | |
P | 11 | 11 | 9 | 9 |
Q | 13 | 16 | 11 | 10 |
R | 12 | 17 | 13 | 8 |
S | 16 | 14 | 16 | 12 |
Machines | Processing time in hours | ||||
A | B | C | D | E | |
M_{1} | 9 | 11 | 15 | 10 | 11 |
M_{2} | 12 | 9 | - | 10 | 9 |
M_{3} | - | 11 | 14 | 11 | 7 |
M_{4} | 14 | 8 | 12 | 7 | 8 |
Machine | Time per unit (in minutes) of product-1 | Time per unit (in minutes) of product-2 | Time per unit (in minutes) of product-3 | Machine capacity (minutes/day) |
{M}_{1} | 2 | 3 | 2 | 440 |
{M}_{2} | 4 | - | 3 | 470 |
{M}_{2} | 2 | 5 | - | 430 |
Property | Property of raw material A | Property of raw material B | Property of raw material C |
Specific gravity | 0.92 | 0.97 | 1.04 |
Chromium | 7 percent | 13 percent | 16 percent |
Melting point | {440}^{0} Celsius | {490}^{0} Celsius | {480}^{0} Celsius |
Food Type | Proteins (yield per unit) | Fats (yield per unit) | Carbohydrates (yield per unit) | Cost per unit (in Rupees) |
1 | 3 | 2 | 6 | 45 |
2 | 4 | 2 | 4 | 40 |
3 | 8 | 7 | 7 | 85 |
4 | 6 | 5 | 4 | 65 |
Minimum Requirement | 800 | 200 | 700 |
Gadget | Foundry | Machine-shop |
A | 10 | 5 |
B | 6 | 4 |
Firm's capacity per week | 1000 | 600 |
Vitamin A | Vitamin B | Vitamin C | Vitamin D | |
Food X | 1 | 1 | 1 | 2 |
Food Y | 2 | 1 | 3 | 1 |
Transportation cost per packet (in Rs) | ||
To \downarrow \ From \to | A | B |
P | 5 | 4 |
Q | 4 | 2 |
R | 3 | 5 |
Cost of transportation (in Rs. per 1000 bricks) | |||
From To | A | B | C |
P | 40 | 20 | 30 |
Q | 20 | 60 | 40 |
Tablets | Iron | Calcium | Vitamin |
X Y | 6 2 | 3 3 | 2 4 |
Nutrient | Fodder 1 | Fodder 2 |
Nutrients A | 2 | 1 |
Nutrients B | 2 | 1 |
Nutrients C | 1 | 1 |
Gadgets | Foundry | Machine shop |
A | 10 | 5 |
b | 6 | 4 |
TIme available (Hour) | 60 | 35 |
Raw material | F_{1} | F_{2} | Availability |
A | 2 | 3 | 40 |
B | 1 | 4 | 70 |
Solve then following LPP graphical method:
Maximize : Z = 7x + y
Subject to : 5x +y \geq 5, x + y \geq 3, x \geq 0, y \geq 0.
Solve then following LPP graphical method:
Maximize : z = 6x + 21y
Subject to : x + 2y \geq 3, x + 4y \geq 4, 3x + y \geq 3, x \geq 0, y \geq 0.
kg per bag |
Brand P | Brand Q | |
Nitrogen | 3 | 3.5 |
Phosphoric acid | 1 | 2 |
Potash | 3 | 1.5 |
Chlorine | 1.5 | 2 |
Food | Vitamin A | Vitamin B | Vitamin C |
X | 1 | 2 | 3 |
Y | 2 | 2 | 1 |
kg per bag |
Brand P | Brand Q | |
Nitrogen | 3 | 3.5 |
Phosphoric acid | 1 | 2 |
Potash | 3 | 1.5 |
Chlorine | 1.5 | 2 |
Type of toys | Machine I | Machine II | Machine III |
A | 12 | 18 | 6 |
B | 6 | 0 | 9 |
Distance (in km) |
From/To | A | B |
D | 7 | 3 |
E | 6 | 4 |
F | 3 | 2 |
A toy company manufactures two types of dolls, A and B. Market tests and available resources have indicated that the combined production level should not exceed 1200 dolls per week and the demand for dolls of type B is at most half of that for dolls of type A. Further, the production level of dolls of type A can exceed three times the production of dolls of other type by at most 600 units. If the company makes profit of Rs.\ 12 and Rs.\ 16 per doll respectively on dolls A and B, how many of each should be produced weekly in order to maximize the profit?
Food | Vitamin A | Vitamin B | Vitamin C |
X | 1 unit | 2 units | 3 units |
Y | 2 units | 2 units | 1 unit |
I | II | III | IV | |
A | 2 | 10 | 9 | 7 |
B | 13 | 2 | 12 | 2 |
C | 3 | 4 | 6 | 1 |
D | 4 | 15 | 4 | 9 |
Strategies | Television | Radio | Magazine-I | Magazine-II |
Cost of an advertising company | Rs.30,000 | Rs.20,000 | Rs.15,000 | Rs.10,000 |
No.of potential customers reached per unit | 2,00,000 | 6,00,000 | 1,50,000 | 1,00,000 |
No.of female customers reached per unit | 1,50,000 | 4,00,000 | 70,000 | 50,000 |
Production Yield | 50-55 | 55-60 | 60-65 | 65-70 | 70-75 | 75-80 |
Number of Farms | 2 | 8 | 12 | 24 | 38 | 46 |
Types of toys | I | II | III |
A | 20 | 10 | 10 |
B | 10 | 20 | 30 |
A | B | |
Grinding | 1 | 2 |
Turning | 3 | 1 |
Assembling | 6 | 3 |
Testing | 5 | 4 |
Machines | |||
I | II | III | |
A | 12 | 18 | 6 |
B | 6 | 0 | 9 |
kg per bag | ||
Brand P | Brand Q | |
Nitrogen | 3 | 3.5 |
Phosphoric acid | 1 | 2 |
Potash | 3 | 1.5 |
Chlorine | 1.5 | 2 |
Area occupied by the machine | Labour force for each machine | Daily output in units | |
Machine A | 1000.sq.\ m | 12\ men | 60 |
Machine B | 1200\ sq.\ m | 8\ men | 40 |
Compounds | Minimum requirement | ||
A | B | ||
Ingredient C | 1 | 2 | 80 |
Ingredient D | 3 | 1 | 75 |
Cost (in Rs) per\ kg | 4 | 6 |
Transportation cost per quintal (in Rs) | ||
To \downarrow \ From \to | A | B |
D | 6.00 | 4.00 |
E | 3.00 | 2.00 |
F | 2.50 | 3.00 |