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Q.1.Mega Marketing is planning a concentrated one week advertising campaign for their new Cuts Everything Super Knife. The ads have been designed and produced and now they wish to determine how much money to spend in each advertising of these two outlets Prime-time TV, and newsmagazines.
For this product, the target
segments are Teenage Boys, Affluent Women (ages 40-49) and Retired Men. Each minute of
primetime TV and page of newsmagazine advertisement reaches the following number of people (in millions).
For this product, the target segments are Teenage Boys, Affluent Women (ages 40-49), and Retired Men. Each minute of primetime TV and page of newsmagazine advertisement reaches the following number of people (in millions)
| Outlet |
Boys |
Women |
Men |
Cost |
| TV |
5 |
1 |
3 |
600 |
| Mag |
2 |
6 |
3 |
500 |
| Target |
24 |
18 |
24 |
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Mega Marketing is interested in straightforward answers like how many units of each
outlet to purchase to meet the segment goals. They are also interested in such questions as "How much will it cost to reach an extra million retired men?", "One radio spot reaches 1 million boys, 1 million women, and 1 million men how much are we willing to pay for such a spot?", and similar questions. Formulate the LPP model.
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Q.2.What is the perfect diet? An ideal diet would meet or exceed basic nutritional requirements, be inexpensive, have variety, and be \pleasing to the palate". How can we
finnd such a diet? Suppose the only foods in the world are as follows:
| Food |
Serving Size |
Energy (kcal) |
Protein (g) |
Calcuim (mg) |
Price (cents/serving) |
Limit (serving/day) |
| Oatmeal |
28g |
110 |
4 |
2 |
3 |
4 |
| Chicken |
100g |
205 |
32 |
12 |
24 |
3 |
| Eggs |
2 Large |
160 |
13 |
54 |
13 |
2 |
| Whole Milk |
237cc |
160 |
8 |
285 |
9 |
8 |
| Cherry Pie |
170g |
420 |
4 |
22 |
20 |
2 |
| Pork & Beans |
260g |
260 |
14 |
80 |
19 |
2 |
After consulting with nutritionists, we decree that a satisfactory diet has at least 2000 kcal of energy, 55 g of protein, and 800 mg of calcium (vitamins and iron are supplied by pills). While some of us would be happy to subsist on 10 servings of pork and beans, we have decided to impose variety by having a limit on the number of servings/day for each of our six foods. What is the least cost satisfactory diet?
Simplex Method
Q.1.Solve the L.P.P.
max
x1 + z2
2x1 +z2 <= 4
x1 + 2z2 <= 3
z1 >=0, x2>=0
Q.2.Solve the L.P.P. by simplex method
Maximise: P=3x+4y subject to:
x + y <= 4
2x + y <= 5
x >= 0, Y >=0
Q.3 Solve the L.P.P. by simplex method
Maximize |
Z = f(x,y) = 3x + 2y |
subject to: |
2x + y ≤ 18 |
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2x + 3y ≤ 42 |
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3x + y ≤ 24 |
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x ≥ 0 , y ≥ 0 |
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Q.1. Find each player's optimal strategy and the value of the two-person zero-sum game
with the following payoff table.
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Player 2 |
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| Player 1 |
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s1 |
s2 |
s3 |
s4 |
| t1 |
{4,-4} |
{5,-5} |
{1,-1} |
{4,-4} |
| t2 |
{2,-2} |
{1,-1} |
{6,-6} |
{3,-3} |
| t3 |
{1,-1} |
{0,0} |
{0,0} |
{2,-2} |
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Q.2.Find the maximin,minimax and value of game.
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Comapany |
Strategies |
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Union |
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I |
II |
III |
IV |
Strategies |
I |
20 |
15 |
12 |
35 |
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II |
25 |
14 |
8 |
10 |
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III |
40 |
2 |
10 |
5 |
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VI |
-5 |
4 |
11 |
0 |
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Q.1. Transportation Problem – Initial Basic feasible solution by N-W method, Row Minima ,Column Minima, LCM, VAM, Optimal Solution
| From To |
A |
B |
C |
SUPPLY |
1 |
4 |
3 |
8 |
300 |
2 |
7 |
5 |
9 |
300 |
3 |
4 |
5 |
5 |
100 |
DEMAND |
200 |
200 |
300 |
700 |
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Q.2. Q.1. Transportation Problem – Initial Basic feasible solution by N-W method, Row Minima ,Column Minima, LCM, VAM, Optimal Solution
From To |
A |
B |
C |
SUPPLY |
1 |
7 |
8 |
6 |
4 |
2 |
9 |
2 |
4 |
3 |
3 |
5 |
6 |
3 |
8 |
DEMAND |
2 |
9 |
4 |
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Q.1.Use Maximax, Minimax regret criteria ,Maximin, Laplace (or Equally Likelihood) Criteria
A management is contemplating the future of one of its plants. Three
alternative decisions are being considered
1. Expand the plant and produce lightweight, durable materials for
possible sales to the military, a market with little foreign competition;
2. maintain the status quo at the plant, continuing production of textile
goods that are subject to heavy foreign competition; or
3. sell the plant now.
The following payoff table describes this decision situation.
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States Of Nature |
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| Decision |
Good Foreign Competitive Conditions |
Poor Foreign Competitive Conditions |
| Expand |
Rs. 800,000 |
Rs. 500,000 |
| Maintain Status Quo |
1,300,000 |
-150,000 |
| Sell Down |
320,000 |
320,000 |
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Q.1 Five men are available to do five different jobs. From the past record the time in hours that each man takes to do the job is known and given in the following table:
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Job1 |
Job2 |
Job3 |
Job4 |
Job5 |
A |
2 |
9 |
2 |
7 |
1 |
B |
6 |
8 |
7 |
6 |
1 |
C |
4 |
6 |
5 |
3 |
1 |
D |
4 |
2 |
7 |
3 |
1 |
E |
5 |
3 |
9 |
5 |
1 |
Find the assignment of men to jobs that will minimize the total time taken. |
Q.2.Given below are estimates of time taken by 4 team member to perform 4 different tasks.How should the tasks be allocated to minimize the total man-hours?
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Task 1 |
Task2 |
Task 3 |
Task4 |
Team member1 |
8 |
26 |
17 |
11 |
Team member2 |
13 |
28 |
4 |
26 |
Team Member3 |
38 |
19 |
18 |
15 |
Team Member4 |
19 |
26 |
24 |
10 |
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Q.3 There are 4 different jobs which can be done by 4 employees.Given below is the matrix form of time in man-hours for each man-job combination.How should the jobs be assigned to minimize man-hours needed?
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JOB 1 |
JOB2 |
JOB3 |
JOB4 |
Employee 1 |
5 |
3 |
2 |
8 |
E2 |
7 |
9 |
2 |
6 |
E3 |
6 |
4 |
5 |
7 |
E4 |
5 |
7 |
7 |
8 |
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Q.1. What do you understand by a queue? Give important applications of queuing theory.
Q.2.Give two examples to illustrate the applications of queuing theory in business and industry.
Q.3.What is a queuing theory problem? Describe the advantages of queuing theory to a business executive. |
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