## Linear Programming Project

Linear Programming Project

Paper details:

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

INFO 2020 Project 2

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 shoulduse 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.