#### Statistics assignment

**Homework 5: OPRE 315**

Please answer the following questions giving all details.

Questions 1 and 3: 1.2 Points each; Question 2: 1.6 Points

- The Charming City Engineering Company is considering five projects for the next year. The number of engineers and the number of support personnel required for each project, and the expected profit for each project are given below.

Project

1 2 3 4 5

_________________________________________________

Engineers Required 28 26 36 31 45

Support Personnel Required 26 28 38 46 36

Profit (in thousands of dollars) 250 320 250 210 350

Formulate a **capital budgeting** problem that maximizes the company’s total profit subject to the following constraints:

– Use no more than 120 engineers

– Use no more than 150 support personnel

– If project 1 is done, then project 2 must be done

– At most four projects can be selected

(a) Define the decision variables.

(b) Determine the objective function. What does it represent?

(c) Determine all the constraints. What does each constraint represent?

**Note: Do NOT solve the problem after formulating.**

- The director of career advising at the Charm City Community College wants to use decision analysis to provide information to help students decide which 2-year degree program they should pursue. The director has set up the following payoff table for four of the most popular and successful degree programs at the college that shows the estimated 5-year gross income (in thousands of dollars) from each degree for three future economic conditions:

**Economic Condition**

**Degree Program Recession Average Good**

Graphic design 165 185 185

Nursing 145 205 225

Real estate 135 205 245

Medical technology 175 175 175

Determine which 2-year degree program to pursue and the profit associated with it by finding the optimal decision using the following decision criteria:

- Maximax
- Maximin
- Equal likelihood
- Minimax regret

- For the problem given in Question 2, the probabilities for the economic conditions are given by P(Recession) = 0.2, P(Average) = 0.4, and P(Good) = 0.4.

** **

- Compute the expected value for each decision and select the best one.
- Compute the expected regret value for each decision and select the best one.
- Calculate and interpret the expected value of perfect information.

- The owner of the Burger Doodle Restaurant is considering two ways to expand operations: open a drive-up window or serve breakfast. The increase in profits resulting from these proposed expansions depends on whether a competitor opens a franchise down the street. The possible profits from each expansion in operations, given both future competitive situations, are shown in the following payoff table:

** Competitor**

**Decision ** Open Not Open

_______________________________________________________

Drive-up window $ – 6,000 $20,000

Breakfast 4,000 8,000

Select the best decision, using the following decision criteria.

- Maximax
- Maximin
- Stevie Stone, a bellhop at the Royal Sundown Hotel in Atlanta, has been offered a management position. Although accepting the offer would assure him a job if there were a recession, if good economic conditions prevailed, he would actually make less money as a manager than as a bellhop (because of the large tips he gets as a bellhop). His salary during the next 5 years for each job, given each future economic condition, is shown in the following payoff table:

** Economic Conditions**

**Decision **Good Recession

_____________________________________________________

Bellhop $120,000 $60,000

Manager 85,000 85,000

Select the best decision, using the Minimax regret decision criteria.

- For information given in Question 2, select the best decision, using the following decision criteria.
- Hurwicz (α= .4)
- Equal likelihood
- Fenton and Farrah Friendly, husband-and-wife car dealers, are soon going to open a new dealership. They have three offers: from a foreign compact car company, from a U.S. – producer of full-sized cars, and from a truck company. The success of each type of dealership will depend on how much gasoline is going to be available during the next few years. The profit from each type of dealership, given the availability of gas, is shown in the following payoff table:

** Gasoline Availability**

**Dealership **Shortage Surplus

.6 .4

______________________________________________________

Compact cars $300,000 $150,000

Full-sized cars –100,000 600,000

Trucks 120,000 170,000

- Determine which type of dealership the couple should purchase using the expected value criterion.
- Determine the expected value of perfect information.
- For information given in Question 4, determine the best decision alternative using the expected opportunity loss criterion.
- Allen Abbott has a wide-curving, uphill driveway leading to his garage. When there is a heavy snow, Allen hires a local carpenter, who shovels snow on the side in the winter, to shovel his driveway. The snow shoveler charges $30 to shovel the driveway. Following is a probability distribution of the number of heavy snows each winter:

**Heavy Snows Probability**

**___________________________________**

1 .13

2 .18

3 .26

4 .23

5 .10

6 .07

7 .03

**Notes:**

–

– Please include all details and steps performed to find your answers. Just writing the final answers will not get you full credit.

– A team submission will be graded based on the answers submitted by the team. If answer to one or more questions is missing because a member of the team did not do his/her part, then the team will not receive any credit for those questions.

– Please submit the homework answers in Microsoft Word Scans or photos of the answers are not acceptable Other formats are not acceptable.