Presentation on theme: "With Vegetable Farm Example"— Presentation transcript:
1With Vegetable Farm Example Extra LP NotesWith Vegetable Farm Example
2Whole Farm Planning Whole-farm planning is largely a matter of enterprise selection. What crops andlivestock enterprises will be produced onthis farm in the next year?
3Background: Enterprise Combinations Economic theory behind whole-farmplanning.
4Production Possibility Curve Definition: A Production Possibility Curve(PPC) is the geometric representation ofthe combination of products that can beproduced with a given set of inputs. Itcan be defined for an entire economy orfor a single firm.
6Types of Enterprise Relationships Competitive with constant substitutionCompetitive with increasing substitutionSupplementaryComplementary
7Competitive with Constant Substitution enterprise 2These enterprises usethe same inputs, in thesame ratios.enterprise 1
8Competitive with Increasing Substitution enterprise 2The enterprises use differentratios of inputs and inputsexperience diminishingmarginal returns in each case.enterprise 1
9Supplementary enterprise 1 makes use of some inputs that are not needed for enterprise 2enterprise 2supplementary rangeenterprise 1
10Complementary enterprise 2 as we produce more of enterprise 1, we can alsoproduce more ofenterprise 2enterprise 1
11Examples Competitive Constant Sub: corn and milo Competitive Increasing Sub:Supplementary:Complementarycorn and milocorn and cottonsoybeans and winter stockersbroilers and cattle
12Terms Physical substitution ratio: Quantity of Output Lost Profit RatioQuantity of Output LostQuantity of Output GainedProfit per unit of gained outputProfit per unit of lost output
13Physical Substitution Ratio The physical substitution ratio is the slopeof the Production Possibility Curve.
14Profit Ratio Profit Ratio is the slope of the isoprofit line: = 1* Y1 + 2 *Y2where 1 is profit per unit of enterprise 1,Y1 is the number of units (e.g. acres)produced, 2 is the profit per unit ofenterprise 2 and Y2 is the number of unitsproduced.
15Decision RulePhysical Substitution Ratio =Price Ratio
16Graph: Point of Tangency enterprise 2isoprofit lines and PPCenterprise 1
17In real life We don't know the PPC. We are going to approximate this process using atechnique called "Linear Programming."
18Linear Programming Linear programming maximizes or minimizes a particular linear objectivefunction, subject to linear restrictions.Here our objective function is to maximizethe returns over variable costs. This is aone-year or short-run plan.
19Returns over variable costs The returns over variable costs come fromthe enterprise budgets.
20Farm Planning Process Inventory available resources Select enterprises to be considered.Obtain appropriate Enterprise Budgets.Figure out the "technical coefficients" and "RHS" (limits)Develop linear programming tableau.Find optimal enterprise combination.
21Resource Inventory The resource inventory tells you how much of each resource (e.g. land, labor,other inputs) you have on the farm.Labor resources is usually calculated forseveral periods of the year. Land may beof several different types.
22Technical Coefficients Technical Coefficients tell you how muchof each resource you need to produce oneunit of a given enterprise.For example, it takes one acre of row-cropland to produce one acre of cotton.
23Restrictions in LP Each limited resource requires one linear restriction in the LP model. Theyare normally "inequality constraints."
24Consider a simple example: Vegetable production in Zaire.Possible enterprises: Lettuce and tomatoes.Each bed of lettuce makes a profit of30 "Zaires" (local currency). Each bedof tomatoes makes a profit of 40 Zaires.
25Marketing Restrictions Marketing: The local market will absorbno more than the output of:16 beds of tomatoes8 beds of lettuce
26Labor Restriction The student who wants to grow vegetables can work up to 24 hours per week on hisgarden.Tomatoes require 1 hour per week.Lettuce requires 2 hours per week.
27Setting up the LP: Objective Function = 1 Y1 + 2 Y2Y1 is the number of tomato bedsY2 is the number of lettuce beds = 40Y Y2
28Restrictions Y1 ≤ 16 (marketing restriction for tomatoes) Y2 ≤ 8 (marketing restriction for lettuce)Y1 + 2Y2 ≤ (labor)So we can produce no more than 16 beds oftomatoes and 8 beds of lettuce. And we mustlimit our labor so that the amount expendedis less than 24 hours per week.
29All Together in Equation Form Objective max 40Y Y2 = Subject to:Y ≤ 16Y2 ≤ 8Y Y2 ≤ 24
30Graphing the constraints lettuce(mktg 1)12(labor)8(mktg 2)2416tomatoes
33Optimizing: Max profit $760 lettuceisoprofit linesslope = -30/40Profit-Max Combination(16,4)8Feasible Region16tomatoes
34With more enterprises With more than two enterprises, we can't graph the solution. We will use somesoftware to find our answer.First we must put the problem in properform.
35Equation Form Again Objective max 40Y1 + 30 Y2 = Subject to: Y1 ≤ 16
36The LP "tableau" Y1 Y2 Type RHS OBJ 40 30 MT1 1 0 LE 16 MT2 0 1 LE 8 LBR LE 24Where LE means less than or equal to andRHS stands for "right hand side"
37The RHS The RHS (right-hand side) contains the amount of the constrained resource youhave available.
38Technical Coefficients The numerical values in the constraint rows,other than the RHS entries, are thetechnical coefficients.
39Objective Function The values in the OBJ row are the amount of profit per unit of enterpriseproduced. In your farm plan, you willget these values from the EnterpriseBudgets.For your OBJ values:Use Returns above Variable Costs.
40Using Excel to Solve the LP I took the tableau for the vegetable example, and solved it using Excel Solver (a tool in Excel). I get the answers 16 beds of tomatoes, 4 beds of lettuce, and profit of $760. If you pop this page open, you can see the formulas I used. You'll learn how to use Solver in the followingslides.