Posted: September 16th, 2017

Please first read ch7, ch8 pages 309-361 and ch9 pages 363-423 on this website –> https://books.google.com.tw/books?id=TTt-BAAAQBAJ&pg=PA363&lpg=PA363&dq=Chapter+9:+Linear+programming:+Applications+in+Marketing,+Finance,+and+Operations+Management&source=bl&ots=6NLDBzIaQJ&sig=ESVGEviaX6K66ZLNn5RZk3PpTgw&hl=en&sa=X&ved=0CCsQ6AEwAmoVChMI_Nyj_ufpxgIVzKOUCh2GHgzH#v=onepage&q=Chapter%209%3A%20Linear%20programming%3A%20Applications%20in%20Marketing%2C%20Finance%2C%20and%20Operations%20Management&f=false

Please first read ch7, ch8 pages 309-361 and ch9 pages 363-423 on this website –> https://books.google.com.tw/books?id=TTt-BAAAQBAJ&pg=PA363&lpg=PA363&dq=Chapter+9:+Linear+programming:+Applications+in+Marketing,+Finance,+and+Operations+Management&source=bl&ots=6NLDBzIaQJ&sig=ESVGEviaX6K66ZLNn5RZk3PpTgw&hl=en&sa=X&ved=0CCsQ6AEwAmoVChMI_Nyj_ufpxgIVzKOUCh2GHgzH#v=onepage&q=Chapter%209%3A%20Linear%20programming%3A%20Applications%20in%20Marketing%2C%20Finance%2C%20and%20Operations%20Management&f=false

AND THEN follow the project instructions under the word document named Tea Making Project Summer Instructions. Please also read the word document named Project 2 Rubrics and make sure all the requirements are met. There are three parts to this project and each part has its own questions within. I have highlighted the important parts inside the word document so please read carefully and answer them. Also include excel files spreadsheet with each part of the project and explanation along with it.

Project 2 – Tea Making
Project 2 – Tea Making
Criteria    Ratings    Pts
Part 1 Objective Function
Is the objective function correct and clearly indicated?    Full Marks

Part 1 Constraints
Are the constraints correct and clearly indicated?    Full Marks
10 pts     No Marks
0 pts
Part 1 answer report
Does the answer report show the correct answer for the given data?    Full Marks
5 pts     No Marks
0 pts

Part 1 Summary of Tea Flavors
Is it clear how many boxes of each type of tea are being made?    Full Marks
10 pts     No Marks
0 pts

Part 1 Limiting Factors
Is it clear what is keeping more of each kind of tea from being produced?    Full Marks
10 pts     No Marks
0 pts

Part 2 New solution – cost
Is the new cost correct for part 2 of the project?    Full Marks
10 pts     No Marks
0 pts

Part 2 Summary of Tea Flavors
Is it clear how many of each kind of tea are being produced?    Full Marks
10 pts     No Marks
0 pts

Part 2 left overs
Is it clear how much of each ingredient is left over?    Full Marks

Part 3 New Solution – Cost
Is it clear what the new solution is in terms of cost?    Full Marks
10 pts     No Marks
0 pts

Part 3 Summary of Tea Flavors
Is it clear how many boxes of each type of tea are produced?    Full Marks
10 pts     No Marks
0 pts
s
Is it clear how much is left of each ingredient?    Full Marks
10 pts     No Marks
0 pts
Dashboard – Easy to read
Is the dashboard well organized and easy to read the solutions (number of boxes made and total profit and cost)    Full Marks
15 pts     No Marks
0 pts

Dashboard Instructions
Do the instructions help a novice user run the optimization?    Full Marks
15 pts     No Marks
0 pts

Dashboard Inputs
Is it clear which cells can be used as inputs to the optimization?    Full Marks
15 pts     No Marks
0 pts

Celestial Seasonings Teas
Celestial Seasonings Teas, headquartered in Boulder, CO, makes a variety of herbal teas (herbal infusions with a variety of ingredients).  They maintain a supply of various ingredients, some of which are more costly than others.  Each day, Celestial Seasonings mixes the appropriate ingredients for the varieties of tea they wish to make and packages the teas in their Boulder factory.
Some of their best-selling herbal teas are as shown in Table 1, along with the chief ingredients for each tea and the amount of each ingredient.
Herbal Tea Name    Ingredients (in grams) per box of 20 tea bags
SleepyTime (ST)    15 gr Chamomile (CH)
13 gr Spearmint (SP)
9 gr Lemon Grass (LG)
5 gr Tilia Flower (TF)
4 gr Blackberry Leaves (BL)
Peppermint (PM)    45 gr Peppermint (PP)
Red Zinger (RZ)    13 gr Hibiscus (HB)
14 gr Rose Hips (RH)
8 gr Peppermint (PP)
6 gr Lemon Grass (LG)
4 gr Orange Peel (OP)
Tension Tamer (TT)    14 gr Eleuthero (EL)
12 gr Peppermint (PP)
9 gr Cinnamon (CI)
6 gr Ginger (GI)
3 gr Chamomile (CH)
3 gr Lemon Grass (LG)
Tangerine Orange Zinger (TZ)    12 gr Hibiscus (HB)
15 gr Rose Hips (RH)
9 gr Blackberry Leaves (BL)
6 gr Orange Peel (OP)
3 gr Tangerine (TG)
Acai Mango Zinger (AZ)    10 gr Hibiscus (HB)
12 gr Rose Hips (RH)
10 gr Orange Peel (OP)
7 gr Acai Berry (AB)
3 gr Mango (MG)
3 gr Blackberry Leaves (BL)
Table 1: Herbal Teas
Each herbal tea is packaged as a box of 20 tea bags for a retail cost of $2.60 per box.  While price is the same no matter the variety, the cost of ingredients varies for each herbal tea based on the type and amounts of ingredients in each.  Table 2 shows the per-gram cost of each ingredient, and how much of each ingredient is in stock and available for mixing:
Ingredient Name    Cost per gram in $    Availability in grams
Hibiscus (HB)    $0.05     8000
Chamomile (CH)    $0.04     10000
Spearmint (SP)    $0.03     10000
Lemon Grass (LG)    $0.04     5000
Tilia Flower (TF)    $0.05     5000
Blackberry Leaves (BL)    $0.03     5000
Rose Hips (RH)    $0.02     15000
Peppermint (PP)    $0.02     15000
Orange Peel (OP)    $0.03     5000
Eleuthero (EL)    $0.07     1600
Cinnamon (CI)    $0.01     5000
Ginger (GI)    $0.03     5000
Tangerine (TG)    $0.02     5000
Acai Berry (AB)    $0.04     4000
Mango (MG)    $0.03     2000
Table 2: Herbal Ingredients
Max Profit
Conditions:
1.    For inventory purposes, Celestial Seasonings must produce at least 100 boxes of each variety of herbal tea.
2.    The supply of Eleuthero has a limited shelf life, and Celestial Seasonings should use 100% of their available Eleuthero today in production. Each gram of Eleuthero not used today still costs $.07, with no additional profits (count the left over and thrown away Eleuthero in the total cost for the day).
Project Part 1:
A.    Set up a Linear Programming model to maximize profit.  Identify the objective function and the formulas for all constraints.
B.    Run the model, and provide a copy of your answer report.
C.    In a summary, identify how many boxes of each tea will be produced (does it make sense to make .73 of a box?) and how much of each ingredient will be left over in inventory.
D.    For each type of tea, identify the limiting factor(s) which prevented Celestial Seasonings from making more of that tea.

Project Part 2:
A.    Maintenance problems have limited today’s production to exactly 1100 units total.  Celestial Seasonings would like to re-run their production model with this limitation in mind, and minimize total costs rather than maximizing profit.  Re-run your model and provide a copy of your answer report.
B.    In a summary, identify how many boxes of each tea will be produced and how much of each ingredient will be left over in inventory.
Project Part 3:
A.    Assume the costs of peppermint and Eleuthero have doubled.  Re-run your project Part 2 model (cost minimization) and provide a copy of your answer report. (don’t limit to 1100 units total)
B.    In a summary, identify how many boxes of each tea will be produced and how much of each ingredient will be left over in inventory.
Assignment Deliverables:
Create a spreadsheet that helps to answer these questions. Create a tab for each Project Part and produce an answer report within each tab. Clearly answer each question that is part of the project. Most importantly, create a dashboard with instructions on how to use the optimization you have created. It should have instructions on what things you could change (Recipes? Costs? Inventories? Other things?). It should have instructions on how to maximize profits. It should be well organized, well labeled, easy to use, and easy to understand.