Description
Ameribank was struggling hard to survive in the market
It decides to conduct a survey as in to analyze the scenario
They decided that a more convenient transaction method must logically succeed the ATM hence the stressed on the use of internet.
CASE : NEW FRONTIERS
Group no.2 Sandhya Nehru 93 Shubham Tiwari 98 Siddharth Dubey 100 Sumoy 105 Smit Shah 101 Nikhil Bansal 119 Vijeesh 111
CASE OVERVIEW
• Ameribank was struggling hard to survive in the market
• It decides to conduct a survey as in to analyze the
scenario • They decided that a more convenient transaction method must logically succeed the ATM hence the stressed on the use of internet.
Question 1
• Formulate a linear
programming model to minimize costs while meeting all survey constraints imposed by Ameribank.
Objective Function:
Min (Z) = 4.75(x11) + 6.5(x12)+6.5(x13)+5(x14)+ 5.25(x21) + 5.75(x22) + 6.25(x23) +6.25(x24) + 6.5 (x31) + 7.5 (x32) + 7.5(x33) + 7.25(x34)
Constraints:
X11 + x12 + x13 + x14 ? 300 (i.e. 15% of 2000)
X21 + x22 + x23 + x24 ? 700 (i.e. 35% of 2000) X31 + x32 + x33 + x34 ? 400 (i.e. 20% of 2000) X11 + x21 + x31 ? 400 (i.e. 20% of 2000) X12 + x22 + x32 ? 550 (i.e. 27.5% of 2000) X13 + x23 + x33 ? 300 (i.e. 15% of 2000) X14 + x24 + x34 ? 300 (i.e. 15% of 2000) X11+x12+x13+x14+x21+x22+x23+x24+x31+x32+x33+x34 = 2000
SOLUTION 1
QUESTION 2
If the profit margin for Sophisticated Surveys is 15 percent of cost, what bid will they submit?
SOLUTION 2
Region 18 to 25 25 to 40 41 to 50 51 and above Percentage of people total customer surveyed
2000
Region
18 to 25
25 to 40
41 to 50
51 and above
Percentage of people surveyed
Silicon Valley
$4.75
$6.50
$6.50
$5.00
300
15
Min. COST
11200
Silicon Valley
600.00
0.00
0.00
300.00
900.00
45
Big cities
$5.25
$5.75
$6.25
$6.25
700
35
Profit margin
1680
Big cities
0.00
550.00
150.00
0.00
700.00
35
Small towns
$6.50
$7.50
$7.50
$7.25
400
20
Bid price
12880
Small towns
250.00
0.00
150.00
0.00
400.00
20
400
550
300
300
850.00
550.00
300.00
300.00
2000.00
Percentage of people surveyed
20
27.5
15
15
cost matrix
42.5
27.5
15
15
Region
18 to 25
25 to 40
41 to 50
51 and above
Silicon Valley Big cities Small towns
$2,850.00 $0.00 $1,625.00
$0.00 $3,162.50 $0.00
$0.00 $937.50 $1,125.00
$1,500.00 $0.00 $0.00
$4,350.00
$4,100.00
$2,750.00
$4,475.00
$3,162.50
$2,062.50 $1,500.00
QUESTION 3
After submitting its bid, Sophisticated Surveys is informed that it has the lowest cost but that Ameribank does not like the solution. Specifically, Rob feels that the selected survey population is not representative enough of the banking customer population. Rob wants at least 50 people of each age group surveyed in each region. What is the new bid made by Sophisticated Surveys?
SOLUTION 3
Region 18 to 25 25 to 40 41 to 50 51 and above total customer
2000
Region
18 to 25
25 to 40
41 to 50
51 and above
Percentage of people surveyed
Silicon Valley
$4.75
$6.50
$6.50
$5.00
300
Min. COST
11388
Silicon Valley
600.00
50.00
50.00
200.00
900.00
45
Big cities
$5.25
$5.75
$6.25
$6.25
700
Profit margin
1708
Big cities
50.00
450.00
150.00
50.00
700.00
35
Small towns
$6.50
$7.50
$7.50
$7.25
400
Bid price
13096
Small towns
200.00
50.00
100.00
50.00
400.00
20
400
550
300
300
850.00
550.00
300.00
300.00
2000.00
cost matrix
42.5
27.5
15
15
Region
18 to 25
25 to 40
41 to 50
51 and above
Silicon Valley Big cities
$2,850.00
$325.00
$325.00
$1,000.00
$4,500.00 $4,100.00 $2,787.50
$262.50
$2,587.50
$937.50
$312.50
Small towns $1,300.00
$375.00
$750.00
$362.50
$4,412.50
$3,287.50
$2,012.50
$1,675.00
QUESTION 4
Rob feels that Sophisticated Survey over sampled the 18 to 25 year-old population and the Silicon Valley population. He imposes a new constraint that no more than 600 individuals can be surveyed from the 18 to 25 year-old population and no more than 650 individuals can be surveyed from the Silicon Valley population. What is the new bid?
SOLUTION 4
Region 18 to 25 25 to 40 41 to 50 51 and above total customer 2000 Region 18 to 25 25 to 40 41 to 50 51 and above Percentage of people surveyed
Silicon Valley
$4.75
$6.50
$6.50
$5.00
650
Min. COST
11388
Silicon Valley
100.00
0.00
0.00
550.00
650.00
32.5
Big cities
$5.25
$5.75
$6.25
$6.25
700
Profit margin
1708
Big cities
400.00
550.00
0.00
0.00
950.00
47.5
Small towns
$6.50
$7.50
$7.50
$7.25
400
Bid price
13096
Small towns
100.00
0.00
300.00
0.00
400.00
20
600
550
300
300
600.00
550.00
300.00
550.00
2000.00
cost matrix
Percentage of people surveyed
30
27.5
15
27.5
Region
18 to 25
25 to 40
41 to 50
51 and above
Silicon Valley Big cities Small towns
$475.00
$0.00
$0.00
$2,750.00
$3,225.00
$2,100.00
$3,162.50
$0.00
$0.00
$5,262.50
$650.00
$0.00
$2,250.00
$0.00
$2,900.00
$3,225.00
$3,162.50
$2,250.00
$2,750.00
QUESTION 5
When Sophisticated Surveys calculated the cost of reaching and surveying particular individuals, the company thought that reaching individuals in young populations would be easiest. In a recently completed survey, however, Sophisticated Surveys learned that this assumption was wrong. The new costs for surveying the 18 to 25 year-old population are listed below. • Region survey cost per person • Silicon Valley $6.50 • Big cities $6.75 • Small towns $7.00 • Given the new costs, what is the new bid?
SOLUTION 5
Region 18 to 25 25 to 40 41 to 50 51 and above total customer
2000
Region
18 to 25
25 to 40
41 to 50
51 and above
Percentage of people surveyed
Silicon Valley
$6.50
$6.50
$6.50
$5.00
300
Min. COST
11588
Silicon Valley
0.00
0.00
0.00
750.00
750.00
37.5
Big cities
$6.75
$5.75
$6.25
$6.25
700
Profit margin
1738
Big cities
0.00
550.00
300.00
0.00
850.00
42.5
Small towns
$7.00
$7.50
$7.50
$7.25
400
Bid price
13326
Small towns
400.00
0.00
0.00
0.00
400.00
20
400
550
300
300
400.00
550.00
300.00
750.00
2000.00
cost matrix
Percentage of people surveyed
20
27.5
15
37.5
Region
18 to 25
25 to 40
41 to 50
51 and above
Silicon Valley Big cities Small towns
$0.00
$0.00
$0.00
$3,750.00
$3,750.00 $5,037.50 $2,800.00
$0.00
$3,162.50
$1,875.00
$0.00
$2,800.00
$0.00
$0.00
$0.00
$2,800.00
$3,162.50
$1,875.00 $3,750.00
QUESTION 6
• To ensure the desired sampling of individuals, Rob imposes even stricter • • • • • • • • • • By how much would these new requirements increase the cost of
requirements. He fixes the exact percentage of people that should be surveyed from each population. The requirements are listed below: Population percentage of people surveyed 18 to 25 25% 26 to 40 35% 41 to 50 20% 51 and over 20% Silicon Valley 20% Big cities 50% Small towns 30%
surveying for Sophisticated Surveys? Given the 15 percent profit margin, what would Sophisticated Surveys bid?
SOLUTION 6
Region 18 to 25 25 to 40 41 to 50 51 and above total customer
2000
Region
18 to 25
25 to 40
41 to 50
51 and above
Percentage of people surveyed
Silicon Valley
$4.75
$6.50
$6.50
$5.00
400
Min. COST
11900
Silicon Valley
0.00
0.00
0.00
400.00
400.00
20
Big cities
$5.25
$5.75
$6.25
$6.25
1000
Profit margin
1785
Big cities
300.00
700.00
0.00
0.00
1000.00
50
Small towns
$6.50
$7.50
$7.50
$7.25
600
Bid price
13685
Small towns
200.00
0.00
400.00
0.00
600.00
30
500
700
400
400
500.00
700.00
400.00
400.00
2000.00
cost matrix
Percentage of people surveyed
25
35
20
20
Region
18 to 25
25 to 40
41 to 50
51 and above
Silicon Valley Big cities Small towns
$0.00
$0.00
$0.00
$2,000.00
$2,000.00 $5,600.00 $4,300.00
$1,575.00
$4,025.00
$0.00
$0.00
$1,300.00
$0.00
$3,000.00
$0.00
$2,875.00
$4,025.00 $3,000.00 $2,000.00
doc_695261404.pptx
Ameribank was struggling hard to survive in the market
It decides to conduct a survey as in to analyze the scenario
They decided that a more convenient transaction method must logically succeed the ATM hence the stressed on the use of internet.
CASE : NEW FRONTIERS
Group no.2 Sandhya Nehru 93 Shubham Tiwari 98 Siddharth Dubey 100 Sumoy 105 Smit Shah 101 Nikhil Bansal 119 Vijeesh 111
CASE OVERVIEW
• Ameribank was struggling hard to survive in the market
• It decides to conduct a survey as in to analyze the
scenario • They decided that a more convenient transaction method must logically succeed the ATM hence the stressed on the use of internet.
Question 1
• Formulate a linear
programming model to minimize costs while meeting all survey constraints imposed by Ameribank.
Objective Function:
Min (Z) = 4.75(x11) + 6.5(x12)+6.5(x13)+5(x14)+ 5.25(x21) + 5.75(x22) + 6.25(x23) +6.25(x24) + 6.5 (x31) + 7.5 (x32) + 7.5(x33) + 7.25(x34)
Constraints:
X11 + x12 + x13 + x14 ? 300 (i.e. 15% of 2000)
X21 + x22 + x23 + x24 ? 700 (i.e. 35% of 2000) X31 + x32 + x33 + x34 ? 400 (i.e. 20% of 2000) X11 + x21 + x31 ? 400 (i.e. 20% of 2000) X12 + x22 + x32 ? 550 (i.e. 27.5% of 2000) X13 + x23 + x33 ? 300 (i.e. 15% of 2000) X14 + x24 + x34 ? 300 (i.e. 15% of 2000) X11+x12+x13+x14+x21+x22+x23+x24+x31+x32+x33+x34 = 2000
SOLUTION 1
QUESTION 2
If the profit margin for Sophisticated Surveys is 15 percent of cost, what bid will they submit?
SOLUTION 2
Region 18 to 25 25 to 40 41 to 50 51 and above Percentage of people total customer surveyed
2000
Region
18 to 25
25 to 40
41 to 50
51 and above
Percentage of people surveyed
Silicon Valley
$4.75
$6.50
$6.50
$5.00
300
15
Min. COST
11200
Silicon Valley
600.00
0.00
0.00
300.00
900.00
45
Big cities
$5.25
$5.75
$6.25
$6.25
700
35
Profit margin
1680
Big cities
0.00
550.00
150.00
0.00
700.00
35
Small towns
$6.50
$7.50
$7.50
$7.25
400
20
Bid price
12880
Small towns
250.00
0.00
150.00
0.00
400.00
20
400
550
300
300
850.00
550.00
300.00
300.00
2000.00
Percentage of people surveyed
20
27.5
15
15
cost matrix
42.5
27.5
15
15
Region
18 to 25
25 to 40
41 to 50
51 and above
Silicon Valley Big cities Small towns
$2,850.00 $0.00 $1,625.00
$0.00 $3,162.50 $0.00
$0.00 $937.50 $1,125.00
$1,500.00 $0.00 $0.00
$4,350.00
$4,100.00
$2,750.00
$4,475.00
$3,162.50
$2,062.50 $1,500.00
QUESTION 3
After submitting its bid, Sophisticated Surveys is informed that it has the lowest cost but that Ameribank does not like the solution. Specifically, Rob feels that the selected survey population is not representative enough of the banking customer population. Rob wants at least 50 people of each age group surveyed in each region. What is the new bid made by Sophisticated Surveys?
SOLUTION 3
Region 18 to 25 25 to 40 41 to 50 51 and above total customer
2000
Region
18 to 25
25 to 40
41 to 50
51 and above
Percentage of people surveyed
Silicon Valley
$4.75
$6.50
$6.50
$5.00
300
Min. COST
11388
Silicon Valley
600.00
50.00
50.00
200.00
900.00
45
Big cities
$5.25
$5.75
$6.25
$6.25
700
Profit margin
1708
Big cities
50.00
450.00
150.00
50.00
700.00
35
Small towns
$6.50
$7.50
$7.50
$7.25
400
Bid price
13096
Small towns
200.00
50.00
100.00
50.00
400.00
20
400
550
300
300
850.00
550.00
300.00
300.00
2000.00
cost matrix
42.5
27.5
15
15
Region
18 to 25
25 to 40
41 to 50
51 and above
Silicon Valley Big cities
$2,850.00
$325.00
$325.00
$1,000.00
$4,500.00 $4,100.00 $2,787.50
$262.50
$2,587.50
$937.50
$312.50
Small towns $1,300.00
$375.00
$750.00
$362.50
$4,412.50
$3,287.50
$2,012.50
$1,675.00
QUESTION 4
Rob feels that Sophisticated Survey over sampled the 18 to 25 year-old population and the Silicon Valley population. He imposes a new constraint that no more than 600 individuals can be surveyed from the 18 to 25 year-old population and no more than 650 individuals can be surveyed from the Silicon Valley population. What is the new bid?
SOLUTION 4
Region 18 to 25 25 to 40 41 to 50 51 and above total customer 2000 Region 18 to 25 25 to 40 41 to 50 51 and above Percentage of people surveyed
Silicon Valley
$4.75
$6.50
$6.50
$5.00
650
Min. COST
11388
Silicon Valley
100.00
0.00
0.00
550.00
650.00
32.5
Big cities
$5.25
$5.75
$6.25
$6.25
700
Profit margin
1708
Big cities
400.00
550.00
0.00
0.00
950.00
47.5
Small towns
$6.50
$7.50
$7.50
$7.25
400
Bid price
13096
Small towns
100.00
0.00
300.00
0.00
400.00
20
600
550
300
300
600.00
550.00
300.00
550.00
2000.00
cost matrix
Percentage of people surveyed
30
27.5
15
27.5
Region
18 to 25
25 to 40
41 to 50
51 and above
Silicon Valley Big cities Small towns
$475.00
$0.00
$0.00
$2,750.00
$3,225.00
$2,100.00
$3,162.50
$0.00
$0.00
$5,262.50
$650.00
$0.00
$2,250.00
$0.00
$2,900.00
$3,225.00
$3,162.50
$2,250.00
$2,750.00
QUESTION 5
When Sophisticated Surveys calculated the cost of reaching and surveying particular individuals, the company thought that reaching individuals in young populations would be easiest. In a recently completed survey, however, Sophisticated Surveys learned that this assumption was wrong. The new costs for surveying the 18 to 25 year-old population are listed below. • Region survey cost per person • Silicon Valley $6.50 • Big cities $6.75 • Small towns $7.00 • Given the new costs, what is the new bid?
SOLUTION 5
Region 18 to 25 25 to 40 41 to 50 51 and above total customer
2000
Region
18 to 25
25 to 40
41 to 50
51 and above
Percentage of people surveyed
Silicon Valley
$6.50
$6.50
$6.50
$5.00
300
Min. COST
11588
Silicon Valley
0.00
0.00
0.00
750.00
750.00
37.5
Big cities
$6.75
$5.75
$6.25
$6.25
700
Profit margin
1738
Big cities
0.00
550.00
300.00
0.00
850.00
42.5
Small towns
$7.00
$7.50
$7.50
$7.25
400
Bid price
13326
Small towns
400.00
0.00
0.00
0.00
400.00
20
400
550
300
300
400.00
550.00
300.00
750.00
2000.00
cost matrix
Percentage of people surveyed
20
27.5
15
37.5
Region
18 to 25
25 to 40
41 to 50
51 and above
Silicon Valley Big cities Small towns
$0.00
$0.00
$0.00
$3,750.00
$3,750.00 $5,037.50 $2,800.00
$0.00
$3,162.50
$1,875.00
$0.00
$2,800.00
$0.00
$0.00
$0.00
$2,800.00
$3,162.50
$1,875.00 $3,750.00
QUESTION 6
• To ensure the desired sampling of individuals, Rob imposes even stricter • • • • • • • • • • By how much would these new requirements increase the cost of
requirements. He fixes the exact percentage of people that should be surveyed from each population. The requirements are listed below: Population percentage of people surveyed 18 to 25 25% 26 to 40 35% 41 to 50 20% 51 and over 20% Silicon Valley 20% Big cities 50% Small towns 30%
surveying for Sophisticated Surveys? Given the 15 percent profit margin, what would Sophisticated Surveys bid?
SOLUTION 6
Region 18 to 25 25 to 40 41 to 50 51 and above total customer
2000
Region
18 to 25
25 to 40
41 to 50
51 and above
Percentage of people surveyed
Silicon Valley
$4.75
$6.50
$6.50
$5.00
400
Min. COST
11900
Silicon Valley
0.00
0.00
0.00
400.00
400.00
20
Big cities
$5.25
$5.75
$6.25
$6.25
1000
Profit margin
1785
Big cities
300.00
700.00
0.00
0.00
1000.00
50
Small towns
$6.50
$7.50
$7.50
$7.25
600
Bid price
13685
Small towns
200.00
0.00
400.00
0.00
600.00
30
500
700
400
400
500.00
700.00
400.00
400.00
2000.00
cost matrix
Percentage of people surveyed
25
35
20
20
Region
18 to 25
25 to 40
41 to 50
51 and above
Silicon Valley Big cities Small towns
$0.00
$0.00
$0.00
$2,000.00
$2,000.00 $5,600.00 $4,300.00
$1,575.00
$4,025.00
$0.00
$0.00
$1,300.00
$0.00
$3,000.00
$0.00
$2,875.00
$4,025.00 $3,000.00 $2,000.00
doc_695261404.pptx