Business Analytics Math Assignment

Submit via BB using Excel.

Save your file using your name. e.g. (BerenIcselDSS610FinalExam)

Please Highlight your final answers. All models shall be functional.

1. Michael Lord has ambitions to be the councilman of Paris, Texas. Mike has determined the breakdown of the steps to the nomination and has estimated normal and crash costs and times for the campaign as follows (times are in weeks).

Mike is not a wealthy man and would like to organize a 16-week campaign at minimum cost. Write and solve a linear program to accomplish this task.

2. 75% of incoming phone-calls to the service desk can be handled by the employee who answers the phone, but the remaining 25% of them will need to be redirected to a subject matter expert. Assume that every call requires one minute of attention by the employee who answers the phone (either to answer the question or to figure out how the referral should be handled). Calls that are redirected need an additional amount of time, as given in the table below.

Callers are served on a first come, first served basis, and are put on hold until the line is free. Use the random numbers to simulate what happens to 10 callers. (Use the random numbers in order - from left to right, first row first - as you need them.) What percentage of your callers needs to be referred? Of those who had to be referred, what is the average referral time?

3. The number of newly listed houses with an estate agent in each quarter over the last four years is given below. Assume the time series has seasonality without trend.

a. Develop the optimization model that finds the estimated regression equation that minimizes the sum of squared error.

b. Solve for the estimated regression equation.

c. Forecast the four quarters of Year 5.

4. The Composite Rotorblade Company (CRC) is gearing up for the new V-280 Helicopter contract. Currently CRC has 100 equally qualified workers. Over the next three months CRC has made the following commitments for blade production:

Each employee can either work in the factory or can train new recruits. A new recruit can be trained to be an apprentice in one month. The next month, he, himself, becomes a qualified worker (after two months from the start of training). Each trainer can train two recruits. The production rate and salary per employee is estimated below.

At the end of July, CRC wishes to have no recruits or apprentices but have at least 140 full-time workers. Formulate and solve a linear program for CRC to accomplish this at minimum total cost.

5. To establish a driver safety school, organizers must decide how many cars, instructors, and students to have. Costs are estimated as follows. Annual fixed costs to operate the school are $30,000. The annual cost per car is $3000. The annual cost per instructor is $11,000 and one instructor is needed for each car. Tuition for each student is $350. Let x be the number of cars and y be the number of students.

Extra Credit

5th grade word problem:

The ratio from Spencer’s age to James’ age is 7:10

Twelve years ago James was twice as old as Spencer.

What will be the ratio of Spencer’s age to James’ age 9 years from now?