3 bussiness question

1

BUS 220- Introduction to Decision Sciences Fall 2015

Assignment 5 due on Tuesday 12/1/2015

NOTE: 10% of your grade will be deducted if the work is not presented in a clear and

neat manner.

NOTE: The assignment could be done jointly by (at most) 2 students. (Of course, it can be

done by a single person.) In any case, the cover page indicating only student(s) names and

student id(s) should be attached to each assignment. I will keep this page for my recording

purposes. The first page of the solutions to the assignment should also include student(s)

names and student number(s), so that you can get the solutions back.

Problem 1 (40 points)

The RMC Corporation blends three raw materials to produce two products: a fuel

additive and a solvent base. Each ton of fuel additive is a mixture of 2/5 ton of material 1

and 3/5 ton of material 3. A ton of solvent base is a mixture of ½ ton of material 1, 1/5

ton of material 2, and 3/10 ton of material 3. RMC’s production is constrained by a

limited availability of the three materials. For the current production period, RMC has the

following quantities of each raw material: material 1, 20 tons; material 2, 5 tons; material

3, 21 tons. Management wants to achieve the following P1 priority level goals.

Goal 1: Produce at least 30 tons of fuel additive.

Goal 2: Produce at least 15 tons of solvent base.

Assume there are no other goals.

a- (10 points) Is it possible for management to achieve both P1 level goals given the constraints on the amounts of each material available?

Explain.

b- (10 points) Treating the amounts of each material available as constraints, formulate a goal programming model to determine the

optimal product mix. Assume that both P1 priority level goals are

equally important to management.

c- (10 points) Use the graphical goal programming procedure to solve the model formulated in part (b).

d- (10 points) If goal 1 is twice as important as goal 2, what is the optimal product mix?

Problem 2 (25 points)

A committee in charge of promoting a Ladies Professional Golf Association tournament

is trying to determine how best to advertise the event during the 2 weeks prior to the

tournament. The committee obtained the following information about the three

advertising media they are considering using.

Category Audience Reached

per Advertisement

Cost per

Advertisement

Maximum Number

of Advertisements

TV 200,000 $ 2500 10

Radio 50,000 $ 400 15

Newspaper 100,000 $ 500 20

2

The last column in this table shows the maximum number of advertisements that can be

run during the next 2 weeks; these values should be treated as constraints. The committee

has established the following goals for the campaign.

Priority Level 1 Goal

Goal 1: Reach at least 4 million people.

Priority Level 2 Goal

Goal 2: The number of television advertisements should be at least 30% of the total

number of advertisements.

Priority Level 3 Goal

Goal 3: The number of radio advertisements should not exceed 20% of the total number

of advertisements.

Priority Level 4 Goal

Goal 4: Limit the total amount spent for advertising to $20,000

a- (10 points) Formulate a goal programming model for this problem. b- (15 points) Use the goal programming computer procedure illustrated in Section

14.2 to solve the model formulated in part (a). Solve the problem with Excel and

submit the computer output.

Problem 3 (35 points)

Here are the gasoline sales time series data:

Week Sales (1000s of gallons)

1 17 2 21 3 19 4 23 5 18 6 16 7 20 8 18 9 22 10 20 11 15 12 22

a.(10 points) To calculate forecasts use a weight of 1/2 for the most recent

observation, 1/3 for the second most recent, and 1/6 for the third most recent and

compute a 3-week weighted moving average for the time series. Calculate the MSE.

b. (10 points) Calculate forecasts by using the 3-period unweighted moving averages

and the corresponding MSE.

c. (10 points) Calculate forecasts by using exponential smoothing with α=0.35

Calculate the MSE.

d) (5 points) Which method do you prefer and why?