operations research assignment unit 3

7/28/2019 Operations Research Assignment Unit 3

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Sri Balaji College of Engineering and Technology, J aipur

Department of Mechanical Engineering

Session (2011-12)

B.Tech. IV Year/VII Semester Subject: - Operations Research

Branch: - Mechanical Engineering Date of assignment: - 20/09/2011

Prepared by: - Mr. Deepak Agrawal Date of submission: - 23/09/2011

Assignment No. 03 (Unit-III)

1. Pizza Hut and Dominos Pizza are two competing restaurants. Each must determinesimultaneously whether to undertake small, medium, or large advertising campaigns.

Pizza Hut believes that it is equally likely that Dominos Pizza will undertake a small, amedium, or a large advertising campaign. Given the actions chosen by each restaurant,Pizza Huts profits are as shown in Table. For the maximin, maximax, and minimaxregret criteria, determine Pizza Huts choice of advertising campaign.

Pizza HutChooses

Dominos PizzaSmall Medium Large

Small 6000 5000 2000Medium 5000 6000 1000Large 9000 6000 0

2. Colaco currently has assets of $150,000 and wants to decide whether to market a newchocolate-flavored soda, Chocola. Colaco has three alternatives:Alternative 1Test market Chocola locally, then utilize the results of the market study to

determine whether or not to market Chocola nationally.

Alternative 2 Immediately (without test marketing) market Chocola nationally.

Alternative 3 Immediately (without test marketing) decide not to market Chocola

nationally.

In the absence of a market study, Colaco believes that Chocola has a 55% chance of

being a national success and a 45% chance of being a national failure. If Chocola is a

national success, Colacos asset position will increase by $300,000, and if Chocola is a

national failure, Colacos asset position will decrease by $100,000.

If Colaco performs a market study (at a cost of $30,000), there is a 60% chance

that the study will yield favorable results (referred to as a local success) and a 40%

chance that the study will yield unfavorable results (referred to as a local failure). If a

local success is observed, there is an 85% chance that Chocola will be a national success.

If a local failure is observed, there is only a 10% chance that Chocola will be a national


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success. If Colaco is risk-neutral (wants to maximize its expected final asset position),

what strategy should the company follow?

3. An art dealers client is willing to buy the paintingSunplant at $50,000. The dealer canbuy the painting today for $40,000 or can wait a day and buy the painting tomorrow (if it

has not been sold) for $30,000. The dealer may also wait another day and buy the

painting (if it is still available) for $26,000. At the end of the third day, the painting will

no longer be available for sale. Each day, there is a .60 probability that the painting will

be sold. What strategy maximizes the dealers expected profit?

4. Solve the following problem by Branch and Bound Technique and Gomorys Cutting Planemethod.

1 2

1 2

1 2

1 2

1 2

7 5 7

12 15 7

, 0

,

MaxZ x x

Subjectedto

x xx x

x x

x x areIntegers

= +

+

5. Solve the following problem by Branch and Bound method.1 2 3

1 2 3

1 2 3

1 2 3

1 3

2 3

4 3 3 6

2 3 3 4

, , 0

,

MaxZ x x x

Subjectedto

x x x

x x x

x x x

x x areIntegers

= + +

+

+ +

6. Solve the following problem by Gomorys Cutting Plane method.1 2

1 2

1 2

1 2

1 2

8 5

6

9 5 45

, 0

,

MaxZ x x

Subjectedto

x x

x x

x x

x x areIntegers

= +

+

+

7. Two prisoners who escaped and participated in a robbery have been recaptured and areawaiting trial for their new crime. Although they are both guilty, the Gotham City district


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attorney is not sure he has enough evidence to convict them. To entice them to testify

against each other, the district attorney tells each prisoner the following: If only one of

you confesses and testifies against your partner, the person who confesses will go free

while the person who does not confess will surely be convicted and given a 20-year jail

sentence. If both of you confess, then you will both be convicted and sent to prison for 5

years. Finally, if neither of you confesses, I can convict you both of a misdemeanor and

you will each get 1 year in prison. What should each prisoner do?

8. Solve the following Game and find the game value.Player A Player B

I II III IVI 3 2 4 0II 3 4 2 4I II 4 2 4 0IV 0 4 0 8

9. An ice cream retailer buys icecream at a cost of Rs. 5 per cup and sells it for Rs. 8 percup; any remaining unsold at the end of the day can be disposed of at a salvage value of

Rs. 2 per cup. Past sales have ranged between 15 and 18 cups per day; there is no reason

to believe that sales volume will take on any other magnitude in future. Find the EMV

and EVPI if the sales history has the following probabilities:

Market Size 15 16 17 18Probability 0.10 0.20 0.40 0.30

10.Solve the game shown in table by the L.P. method.Player A Player B

I II IIII 3 -4 2I I 1 -3 -7I II -2 4 7

operations research assignment unit 3

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