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Minnesota Agriculture in the Classroom

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Food for Thought Lesson Plans

Weber's Least Cost Theory

Grade Level

Grades 9-12

Purpose

The purpose of this lesson is to initiate students into Weber's Least Cost Theory by giving them practical application of the theory with a bulk-reducing industry (ethanol) in the state of Minnesota.

Time

Three 50-minute class periods including previous Weber Lesson on MN Ag in the Classroom website

Materials
Vocabulary
  • Weight-Gaining Industry: An industry in which the final product weighs more than the raw materials
  • Weight-Reducing Industry: An industry in which the final product weighs less than the raw materials
  • Bulk-Gaining Industry: An industry in which the final product has more space than the raw materials
  • Bulk-Reducing Industry: An industry in which the final product has less space than the raw materials
  • Transportation: The movement of goods by means of either highway (truck), rail (train), air (airplane), pipeline, or water (ships)
Background—Agricultural Connections

Many factors are taken into consideration by businesses when determining the location of their production facility/factory or store. One of the biggest considerations regarding these items is the distance the factory/store is from the market and natural resources used. Use Weber's least cost model to determine which counties in Minnesota would be the best location to build production facilities that support Minnesota agriculture. Students will consider many factors in determining their location, especially distance and transportation.

Weber's Model of Impact of Transport Costs

This model is intended to help geographers determine where to locate factories based on the costs of shipping goods.

This model is used to help predict what other factors might be important in the location of economic activities.

Explanation of Weber's Model
  1. The model is used to analyze a single isolated country that is homogeneous in terms of climate, topography, population, and under one political authority.
  2. Some natural resources (for instance water and sand) are ubiquitous (found everywhere) whereas others (such as coal and iron ore) occur only in fixed locales (found only in a set location).
  3. Available workers are not ubiquitous; rather they are fixed in specific places.
  4. Transportation costs are a function of weight and distances increasing in direct proportion to the length of shipment and weight of cargo.
  5. Manufacturing plants will be located, in response to three forces: relative transport costs, labor costs, and agglomeration (a collection of industries, factories, etc., in one location).
Case 1: One Market and One Raw Material
  • If the raw material is ubiquitous, then the factory will locate at the market.
  • If the raw material is fixed and no weight is lost in the manufacturing process, the factory can locate at either the market or the source of raw material.
  • If the raw material is fixed and weight is lost in the manufacturing process, the factory will locate at the source of raw material.
Case 2: One Market and Two Raw Materials (R1 and R2)

If customers for a product are in only one place and the product is manufactured from two raw materials (R1 and R2), then manufacturing will tend to locate in one of the following ways:

  • If both R1 and R2 are ubiquitous, then manufacturing will be at the market.
  • If R1 is ubiquitous and R2 is fixed elsewhere than at the market, and if both are pure (no weight loss), then manufacturing will be at the market.
  • If both raw materials are fixed and pure (neither resource has other materials in it which results in no weight loss), the factory will be at the market.
  • If both raw materials are fixed and gross (contains other materials which have to be removed resulting in weight loss), the solution is complex, and Weber introduced his famous locational triangle (see diagrams below).
Diagrams

Suppose R1 and R2 lose 50% of their weight in the manufacturing process and 2,000 tons of each are required a year. If the factory were located at M, the total transportation costs would be (A) 2,000 tons X 100 miles = 200,000 ton miles on R1 from R1 to M, plus (B) 200,000 ton miles on R2 from R2 to M or 400,000 ton miles in all.

However, if the factory were located at Point X, midway between R1 and R2, the transportation burden would be as follows: (A) 2,000 tons X 50 miles = 100,000 ton miles on R1 from R1 to X, plus (B) another 100,000 ton miles on R2 from R2 to X, plus (C) 2,000 tons X 87 miles = 174,000 ton miles on finished product from X to M or a total of 374,000 ton miles. This is less than the burden facing an industry at either M or R1 or R2.

If the two raw materials do not have the same weight loss or if different amounts are required, the factory would tend to locate nearer one of the raw material sources so as to lessen the burden of transportation costs. See Weber Model Case 2 Handout for use with additional clarification on calculations.

When applying the model to Minnesota agriculture and agribusiness, it is important to remind students that most processes involve weight loss and bulk reduction. However, bottling liquid milk for direct consumption is bulk gaining and in addition, it must be delivered quickly to both the bottling plant and consumers. Grain shipping does not involve loss of weight or bulk. Ethanol involves weight and bulk loss but the byproduct (corn mash) can be sold for animal feed and so has a separate set of transport variables.

Interest Approach - Engagement

Tell students that they have been selected to serve on a state-wide task force to determine what counties are interested in developing industrial facilities to support Minnesota agriculture.

In developing their opinions, the students should make the following assumptions:

  1. There will be enough labor in each of the interested communities or labor will move to the communities to take the new jobs created. Labor costs will be essentially the same in all locations.
  2. There is both a state and national market for the goods produced.
  3. The basic geography of the production of crops and livestock will not change during the time the task force is deliberating.
Procedures
Part 1: Introduction into Weber's Model

In order to facilitate the students resolving this issue, the teacher should lead the entire class through an example of how to determine the effects of transport on the processing operations using map layering techniques. Teachers should select any commodity in which they have a special interest. The example of milk is provided because most students will have some familiarity with it.

  1. Activate prior knowledge by asking the students what they know about the production of milk and how it is processed. Discussion should include:
    1. Milk comes from cows.
    2. Milk can spoil or turn sour quickly.
    3. Milk is sold in small volumes directly to the consumers – bottle, carton, etc.
    4. The number of dairy farms is decreasing due to the economies of scale (cost advantages due to size of farm) that can be realized by large producers. Note: Large producers milk 700 to 1,000 cows thus producing more milk than farmers with 50 cows.
    5. Milk is shipped from farm to processing plant in tanker trucks.
    6. Milk must be kept chilled between the time it leaves the cow until it is processed to prevent spoilage.
  2. Show the following maps to the students and ask the students to explain the distribution of cows in Minnesota: Dairy Cows in Minnesota Counties (Map 9), Corn for Grain in Minnesota Counties 2017 (Map 4), Soybeans in Minnesota Counties 2017 (Map 6), All Hay in Minnesota Counties (Map 8), Alfalfa in Minnesota Counties (Map 7) and Major Cities and Waterways (Map 40).
    1. Dairy farms are concentrated in areas that are not primary production zones for grain because the cattle can graze on hilly pastures unsuitable for grain.
    2. Dairy farms are generally near the urban areas.
    3. Most dairy farms are not found in the cold forested region of Northern Minnesota.
  3. Compare the map of Milk Production (Map 10) with the map of Dairy Cows in Minnesota Counties (Map 9) and ask the students to explain what correlations exist between the two maps.
  4. Compare the map of Dairy Product Processing Sites in Minnesota (Map 29) to the map of Milk Production (Map 10) and the Major Cities and Waterways (Map 40). Next, using the discussion of Weber's model, ask the students to explain the distribution of bottled milk plants.

    Students should note that of the 13 bottling plants in the state, 10 are located near markets. This can be explained by using the model and what they know about the production and processing of "bottled" milk.
    • If the raw material is ubiquitous (found everywhere), then the factory will be located at the market.
    • If the raw material is fixed (only in one location), and no weight is lost in the manufacturing process, the factory can locate in either the market or at the source of raw material.
    Diagrams
  5. Using the map of Dairy Product Processing Sites (Map 29) and your discussion of Weber's model, ask the students to explain the distribution of butter, cheese, or ice cream plants.

    Students should note that of the 24 plants in the state, four are obviously located near markets. This can be explained by the students using the model and what they know about the production of these products. Because all three of these products reduce the bulk of the fresh milk and the product is less perishable than milk, they may locate plants in locations that will reduce the transportation costs of the fresh liquid milk. The refrigerated products can then be shipped great distances.
    • If the raw material is fixed (in one location) and weight is lost in the manufacturing process, the factory will locate at the source of raw material.
Part 2: Task Force Actions
  1. Divide the class into "task force subcommittees". Give each student or subcommittee a Task Force student handout.
  2. Assign each subcommittee a commodity (agricultural product) and processing operation from those listed below to analyze. Instruct students to use the appropriate maps and aspects of the model to identify the counties that are NOT efficient location sites and the county that best meets the locational criteria.
  3. After analyzing their maps, the students are to prepare a one-page report which summarizes how they came to their conclusion and makes reference to the maps they used to develop their conclusion. Students should also use principles of Weber's model in defending their location in their conclusion.
The task force subcommittee assignments are as follows:
  • Group 1: Koochiching, Stearns, Brown, Norman, Kandiyohi, and Houston counties have applied for a grant to build an ethanol plant with a capacity of thirty million gallons per year. In which of these counties would such a facility be most likely to succeed and why?
  • Group 2: The counties of Polk, Pine, Sherburne, Stearns, Anoka, and Cottonwood have applied for a grant to develop an apple processing plant. In which of these counties would such a facility be most likely to succeed and why?
  • Group 3: The counties of Morrison, Crow Wing, Martin, Clearwater, Pipestone, and Faribault have applied for a grant to develop a beef processing plant. In which of these counties would such a facility be most likely to succeed and why?
  • Group 4: The counties of Rock, Chippewa, Meeker, Houston, Blue Earth, and Hennepin have applied for a grant to have a pork processing plant. In which of these counties would such a facility be most likely to succeed and why?
  • Group 5: The counties of Hennepin, Ramsey, Carlton, Isanti, Chisago, and Martin have applied for a grant to establish a turkey processing plant. In which of these counties would such a facility be most likely to succeed and why?
  • Group 6: The counties of Hennepin, Ramsey, Carlton, Isanti, Chisago, and Martin have applied for a grant to establish a chicken processing plant. In which of these counties would such a facility be most likely to succeed and why?
  • Group 7: The counties of Carver, St. Louis, Hennepin, Yellow Medicine, Benton, and Stevens have applied for a grant to establish a vegetable canning and freezing plant. In which of these counties would such a facility be most likely to succeed and why?
Assessments
  1. Each subcommittee will select a representative to report back to the task force-at-large (class). Each subcommittee will prepare a map of the location they selected for their production facilities and share with the task force-at-large (class). The representatives of each subcommittee will explain to the task force-at-large the rationale behind the location of their production facilities. After each committee's presentations, the teacher will show the current map of the production facilities for their specific product and the class will analyze how close the subcommittee's selected county is to the current production centers. If the subcommittee's selection and the existing pattern are different, have the students discuss why the difference exists. This discussion should help to clarify for the students how Weber's industrial location model was used.
  2. If time allows, ask students to individually come up with a rebuttal statement against one of the sites selected which includes at least three specific reasons why the selected location is not the best location for that production facility.
Part 3: Investigating Weight-Bearing and Weight-Reducing Industries
  1. Show an image from a local gas station. Ask students, who are drivers or who have visited a gas station with a driver, what they have noticed in their options of fuels to use in their vehicles. Answers may include diesel, unleaded, unleaded plus (E15, gasoline with 15% ethanol), E85 (51-83% ethanol with gasoline), etc., and also the cost (E85 is usually less expensive). Explain that most gasoline in the state of Minnesota has some type of ethanol in it. Per MN Stat 239.791, all gasoline must have the highest approved biofuel composition in gasoline, which is currently ethanol at 10%. All gasoline, all grades (regular, midgrade, premium) MUST have 10% ethanol (officially it is between 9 and 10%). Ethanol free fuel, also known as non-oxygenated gasoline, can be sold for collectible cars, marine applications, and some other things, but it must be labeled for these special applications and must be premium (high octane, 91 or higher) fuel. Outside of those applications, premium fuel should also have 10% ethanol in it.
  2. Show students the Ethanol Production in Minnesota (Map 27) and Corn for Grain in Minnesota Counties 2017 (Map 4). Have students work independently or in pairs or small groups to determine whether the ethanol industry is weight-gaining or weight-reducing. Allow groups to explain their answers.
  3. Next, give/project students the Major Meat Processing Plants in Minnesota (Map 30) which includes the beef and pork plants in the state of Minnesota. Also provide the Beef Cattle in Minnesota Counties (Map 11) and Hogs and Pigs in Minnesota Counties (Map 12). Once again, have students work in groups or independently to determine whether the meat packing industry in weight-gaining or weight-reducing. Students should explain why this is the case.
Answers

Both ethanol and meat packing industries are weight-reducing industries. Most of the factors are the high bulkiness of the raw materials coming in (i.e., corn and animals) compared to the finished products (ethanol/liquid and meat). Since producers want to minimize transportation costs, they would want to reduce transporting the heavier products further such as bulky corn and heavy cows. Therefore, the production plants are going to be located closer to the growing areas of each product since they would rather haul the lighter finished product further to reduce transportation costs.

Local Flavor
  • Students should look at processing plants or factories around their local area. Students should ask the following questions regarding that processing in their area: What are they producing? What are their raw materials? Is the process weight-gaining or weight-reducing? Is the process bulk-gaining or bulk-reducing?
  • Where is the primary market for the factory?
Did you know? (Ag Facts)
  • Minnesota is the largest turkey producing state in the country with over 42 million turkeys in 2017 (USDA).
Minnesota Academic Standards
Social Studies - Geography

9.3.2.4.1 Apply geographic models to explain the location of economic activities and land use patterns in the United States and the world.

9.3.2.4.2 Identify the primary factors influencing the regional pattern of economic activities in the United States and the world.

9.3.2.4.4 Describe patterns of production and consumption of agricultural commodities that are traded among nations.

Common Core Connections
Grade 9-12 Literacy in History/Social Studies

CCSS.ELA-LITERACY.RH.9-10.7
Integrate quantitative or technical analysis (e.g., charts, research data) with qualitative analysis in print or digital text.