Project-1

---

Marking criteria

---

The marking depends on the correctness of the answers and clarity of the written report. Make sure you report clearly your hypothesis, conclusions and the necessary interpretation of any output in a clear way. You need to provide and present the work in a clear, concise and objective way. Maximum mark=40 marks

---

Problem 1 [ 5 marks]

---

Company, which manufactures makes hockey sticks and chess sets.Each hockey stick yields an incremental profit of $5, and each chess set, $5.

---

- A hockey stick requires 6 hours of processing at Machine Center A and two hours at Machine Center B. A chess set requires 6 hours at Machine CenterA, 8 hours at Machine Center B, and 2 hours at MachineCenter C.

---

- Machine Center A has a maximum of 60 hours of available capacity per day, Machine Center B has 36 hours, and Machine Center C has 10 hours.

---

If the company wishes to maximize profit, how many hockey sticks and chess sets should be produced per day?

---

Answer the following:

---

a) Formulate the linear programming model to determine the optimal solution

---

b) Use Excel solver to generate the sensitivity report and Interpret the sensitivity report.

---

c) Use Solvertable to investigate further the sensitivity of the various input (discuss)

---

Problem 2 [ 5 marks] L.P. : Scheduling Problem

---

A commercial Airline in the UAE has 4 flight attendants that it wants to assign 4 monthly schedules in a way to minimize the number of nights they will be away from home. The numbers of night each attendant must be away from home with each schedule is given in the following table:

---

Identify the optimal scheduling in order to minimize the total number of nights the attendants will be away from home

---

Problem 3 [ 5 marks]

---

For a given business the cost of an emergency generator is $400,000. In case it is installed there is no loss from power failure. There is 14% chance of power failure. In case there is power failure there is a probability of 0.06 that the loss would be $35 millions. And there is probability of 0.94 that the loss would be only $600,000. Determine whether the business should build the emergency generator. Use treePlan to check your answer.

---

Problem 4 [ 5 +5 =10 marks]

---

Suppose you have three options to start a business near a good mall that attracts students: Opening a medium-sized shop, or a small shop or no shop at all. The market can be good, average or bad. The probabilities for these three possibilities are 0.2 for a good market, 0.5 for an average market, and 0.3 for a bad market. The net profit or loss for the three business options are given in the following table.

---

Part A

---

a) Construct a decision tree for this problem.

---

b) If the decision maker knows nothing about the probabilities of the states of nature, find the recommended decision and the corresponding profit using:

---

b1) Optimistic approach

---

b2) Conservative approach

---

b3) Minimax regret approach

---

c) Suppose that the decision maker obtained the probabilities P(good market) = 0.2, P(average market)=.50, and P(bad market)=0.3,

---

c.1) What is the recommended decision using the expected value approach? (explain).

---

c.2) What is the optimal decision(s) if perfect information were available? What is the expected

---

value of perfect information? Interpret it. [ optimal decision(s) if perfect information were available, EVwPI( Expected value with Perfect Information, EVPI ( Expected value of perfect information] d) Carry the sensitivity analysis describing how changes in the state-of-nature probabilities affect the recommended decision alternative.

---

Part B

---

Market research firm offer to perform a study at a fee of 5 K $.

---

P(GoodMarket | Positive Report) = 0.65

---

P(Average-Market | Positive Report) = 0.25

---

P(Average Market | Negative Report) = 0.30

---

P(Bad Market | Negative Report) = 0.48

---

a) Develop a new decision tree

---

b) Course of action

---

c) How much might the will you be willing to pay for the market research?

---

Problem 5 [ 10 marks]

---

We need to build up to 6 power plants (L1 to L6) to serve 7 communities (C1 to C7). The cost to build a power plant is 6.5 million (AED). The maximum capacity of each plant is 11 million watts. The demand of each community is given below:

---

The benefits (in $/watt but sometimes it is a loss) from serving the community is given below:

---

community 1 2 3 4 5 6 7

---

Demand in

---

millions watt

---

3 4 6 4 5 2 4 3 Find which power plants should be built.

---

Problem 6 [ 5 marks]

---

Use simplex method to solve the following LP

---

Minimize

---

40 x+50 y

---

Constraint to:

---

3 x + 5 y ≥ 150

---

5 x + 5 y ≥ 200

---

3 x + y ≥ 60

---

All decision variables are non-negative