Highlights
1. Part A: Hope is an Indian company. Hope produces two different products (Music and Dance). Both the products require three different resources (Love, Peace and Harmony). The table shows the availability of the resources and their requirement in appropriate units.
The objective of Hope is to maximize profits. What best combination of Music and Dance should Hope produce to achieve the objective? (I hope that the table is self-explanatory.) Part B: In a linear programming context, explain briefly - through example graphs - the case of
Unboundedness
Infeasibility
Multiple Optima
2. Part A: Explain the basics of Goal Programming technique through an example of your Describe briefly the two methods employed to solve a Goal Programming Problem. Part B: What are the three essential elements of an optimization problem?
3. A Transportation Problem is described by the following self-explanatory table. Solve it through, a) North West Corner Method; b) Least Cost Method; c) Vogel’s Approximation
|
|
City A |
City B |
City C |
City D |
Supply |
|
Warehouse X |
10 |
2 |
20 |
11 |
15 |
|
Warehouse Y |
12 |
7 |
9 |
20 |
25 |
|
Warehouse Z |
4 |
14 |
16 |
18 |
10 |
|
Demand |
5 |
15 |
15 |
15 |
|
4. Zed and Adrian and run a small bicycle shop called "Z to A Bicycles". They must order bicycles for the coming season. Orders for the bicycles must be placed in quantities of twenty (20). The cost per bicycle is $70 if they order 20, $67 if they order 40, $65 if they order 60, and $64 if they order 80. The bicycles will be sold for $100 each. Any bicycles left over at the end of the season can be sold (for certain) at $45 each. If Zed and Adrian run out of bicycles during the season, then they will suffer a loss of "goodwill" among their They estimate this goodwill loss to be $5 per customer who was unable to buy a bicycle. Zed and Adrian estimate that the demand for bicycles this season will be 10, 30, 50, or 70 bicycles with probabilities of 0.2, 0.4, 0.3, and 0.1 respectively.
Actions
There are four actions available to Zed and Adrian. They have to decide which of the actions is the best one under each criterion.
Zed and Adrian have control over which action they choose. Payoff table for this scenario is given below:
|
Alternatives |
|
Buy 20 |
Buy 40 |
Buy 60 |
Buy 80 |
|
State of Nature |
|
||||
|
Demand 10 (0.2) |
50 |
-330 |
-650 |
-970 |
|
|
Demand 30 (0.4) |
550 |
770 |
450 |
130 |
|
|
Demand 50 (0.3) |
450 |
1270 |
1550 |
1230 |
|
|
Demand 70 (0.1) |
350 |
1170 |
2050 |
2330 |
|
Based on this information, answer following questions:
What will be your best decision in this situation using the following approaches?
Maximin Criterion
Maximax Criterion
Minimax Criterion
5. You are planning to buy a mobile phone. You have three options (A to C). You may take decision on four criteria (Cost, Storage, Camera and Looks). The table below summarizes the available
|
|
Price in $ |
Storage in GB |
Camera in MP |
Looks |
|
Brand A |
250 |
16 |
12 |
Excellent |
|
Brand B |
200 |
16 |
8 |
Average |
|
Brand C |
300 |
32 |
16 |
Good |
You may use the following scores to convert a subjective criterion into objective value: Excellent (5), Good (4), Average (3), Bad (2) and Worst (1). You may use the following weights for different criteria: Price (0.3), Storage (0.2), Camera (0.2) and Looks (0.3). Use the method of TOPSIS to select the best mobile phone.
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