Applications of mathematical programming on four New Zealand horticultural holdings : a thesis presented in partial fulfilment of the requirements for the degree of Master of Horticultural Science in Massey University

(1)

Copyright is owned by the Author of the thesis. Permission is given for

a copy to be downloaded by an individual for the purpose of research and

private study only. The thesis may not be reproduced elsewhere without

the permission of the Author.

(2)

APPLICATIONS OF MATHEMATICAL PROGRAMMING

ON FOUR NEW ZEALAND HORTICULTURAL HOLDINGS

by

.1-,.N. RAE

Thesis Presented in Partial Fulfilment of the Requirements for the Degree

of

Master of Horticultural Science in

Massey University

November

1968

(3)

ACKN OVJLEDG EM ENT S

The author wishes to thank his two supervisors, Professor W.V.

Candler and his successor, Professor A.R. Frampton, for their advice and encouragement received during this study. Special thanks are due to Professor Candler who obtained a solution to the quadratic

programming study of Chapter 5 at Purdue University, Indiana, U.S.A.

But for a lack of time a solution to the quadratic programme of Chapter

6

would have been obtained from the same source.

The author also wishes to express his thanks to the four

horticulturalists who willingly gave of their time to allow the various programming models to be constructed.

Thanks are due to tiesdames J . Bishop and .M. Clifford for typing, and to the library staff for their assistance in obtaining references.

Finally, thanks are due to members of the Horticulture Depart- ment, Massey University, with whom the author had discussions from

time to time.

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CH.Ai=-T.iR 1 1. 1 1. 2 1-3

1. 4

CH .• .r-T.,.,..R 2 2 .1

CHAFT:C:R 3

Quadratic rogramming 2.2.1.

2.2.2

2.2.3 2.2.4 2.2.5 2.2.6

2.2.7 2.2.7.1 2.2.7.2 2.2.7.3 2.2.7.4

Introduction

Statement of the quadratic programming problem

The related lagrangian problem The partial derivatives

The related linear programming problem An algorithm for solving quadratic

programming problems

Interpretation of the solution Real activities in the basis Real ~ctivities not in the basis Imputed values of scarce resources Resources in disposal

Risk Programming 2.3.1

2.3.2

2.3.3 2.3.4

2.3.5

Introduction

Some examples of stochastic errors in horticultural production data

An outline ofrisk programming A measure of risk

Mathematic_l statement of the risk programming froblem

LIT E:,R l .aOGRnMMING ND PROFIT MAXIMIS.'-.TICN N ,,N GT~.KI HORTICULTUal,L HOLDING

3.1 Introduction

3.2 ~ Descrii tjon oft~~ Holding 3.2.1

3. 2.2 3. 2-3

3.2.4

3. 2. 5 3. 2 . 6

3.2.7

Location s~ze Leased land

Glasshouse area Cropping ~ractice Soil ty}Jes

Rainfall and irrigation Disease problems

3.3 The Restraints 3.3.1

3.3.2

3. 3 . 3

3.3.4

3 . 3 . 5

Problems of timing of production Freehold land (restraints R1-R7) Leased land (restraints R8-R15)

Labour availability (restraints R16-R39) Cropping limits (restraints R40-R52)

19 19 20 22

22 25 25 25 25

25 25 25

27 28

30

32

35 35 35 35 36 36 37 37 39 3'3 40 42

(6)

3.4

3,5

The Activities 3.4.1

3,4.2 3.4.3

3.4 . 4 3.4 . 5

3.4.6

3.4 . 7

3.4.8

3.4.9

3.4.10 3.4.11 3.4.12 3.4.13

3.4.14

Production on leased and freehold land Cauliflower (P1)

Cucumber (P2) Tomato (P3) Lettuce (P4)

Pumpkin (P5 and P10) Rhubarb (P6)

Soleil d'Ors (P7) Lettuce (P8)

Carrot (P9) Cucumber ( P11) Cabbage (P12) Cauliflower (P13)

Glasshouse cucumber (P14) The Objection Function

3. 5

.1 3.5.2 3.5.2.1 3.5.2.2 3.5.2.3 3.5.3

3.5 . 3 .1

3.5.3.2

3.5.4

3.5.4.1 3.5.4,2

3.5.5

Introduction

Calculation of gross margins Expected prices and yields Variable costs

Gross margins

Perennial crops and discounting Present value of rhubarb (P6) Present value of Soleil d'Ors (P7) Calculation of annuities

Rhubarb (P6) annuity Soleil d'Ors (P7) annuity Overhead costs

3.6 Input-Output Coefficients

3.6.1 Freehold land restraints 3.6.2

3.6 . 3 3.6.4 3 . 6.4 . 1 3. 6 . 5

Leased land restraints Labour restraints

Cropping limit restraints The glasshouse r estraint (R52) Dominated restraints

3.7 The Basic Matrix

43 43

44 44 45

46 46 46 46

47

48

48 48 49 49 50

50 52

52 54 54

56

59 59

60 60 61 61 61 63

65

65 66

66

(7)

3 . 8

3. 9

The Solution

68

3. 8. 1 68 3.8. 2 3. 8. 2. 1 3 . 8.2. 2 3. 8. 3 3. 8. 4 3 . 8 . 4. 1 3.8 . 4. 2 3. 8. 5 3. 8. 5. 1 3 . 8.5 . 2 3. 8.5.3

The cropfing programme

Corn_p1rison of the linear programme solution with the grower's plan Comparison of activity levels Com~arison of pr ofits

Stability of the o~timum plan Unused resources

Land Labour

Value of resources Land

Labour

Cropping l imits

68 68

71

3.8 . 5 . 3 . 1

The tomato cropping limit A Parametric Solution

71

73 73 74 75 75

76 76 77

77

3.9 . 4

The reason for comfuting al ternative plans

77

Parametric linear programming 77 Activity levels i n the parametric

solution 79

Resource values in the ~arametri c solution 79 Su~~lementary, complementary and

competitive relationships within the

parametric solution

82

3 . 10

Adopti on by the Grower of a Linear rrogramme Solution

3.10 . 1 3. 10 . 2 3.10 . 2. 1 3 .1 0 . 2. 2 3. 10 . 2.3 3. 10 . 3 3. 10.3 . 1 3 . 10.3.2 3 . 10.3 . 3 3 . 10 . 4 3 . 10.4 . 1 3.1 0. 4.2

Introduction

Comparison of the adopted plan with the grower's plan

Comparison of activity levels Comparison of profits

Comparison of resource requirements Stability of the adopted plan

Stable components of the plan Unstable components of the plan Crop which may become profitable Unused resources

Land Labour

86

88

91 91

93

94

95

96

(8)

3.10.4 .2.1

Overhead labour

3 .1 0 . 4 . 2.2

Replanting ferennial crops Value of resourceG

3 .1 1

Increased 1rofits and T&xation

3 . 12

Gro,ver 's Comments on the 1 rogramming Solutions

3 .12.1 3.12 .2

3 .1 2.4

CH •

.:..1

T....R 4

Physical plans

Hesource dis~os&l levels .::>hadov; iJrices

Further com~~nta on .he udo~ted ~lan I:rV.c...3TLc.N1 I:~ f...,..:(t,N1~LiL CRC10 - J. C · • .t IT . .'.,.L BUDG:TIXG , DTE"iT..;:,iFORAL LL~ r:.. R .t-ROG1id.;;'i£

4 . 1

Introduction

4. 1 .1 4.1.2 4.1.3

The reason for ~n intertem~oral a~proach Brief review of intertem~oral

pr ogramming in f~rm lll3.nagement An outline of the intertemporal

programming m~trix

4 . 2

De&cription of the Holding

4.2 . 1

4.2.2

4 . 2.3 4.2.3 . 1

4.2.4

4 . 2 . 5 4. 2 . 6 4 . 2 . 7

~ocation and size

?re~~nt cro1~ing ~r~ct~ce Future crG;:in6 ~rcctice

Treatment of tre young aprle ~~i

young as¥araguF cror~ ir. the model Intercro.t-·ping

Soil tyres Irrication

Disease 1·0 blems

4 . 3

The Restraint~

4.3 .1

4.3.2

4 . 3 . 3

4. 3 .4

4.3.5

4.3 . 6 4 . 3 . 6.1 4. 3 . 6 . 2

4 . 3 . 6 . 4

Land Laoour

CrofS grown under contract for processing

Restrict ions on fresh market crops Rotation restraints

Cash and taxation restr~ints

Treatment of cash flows in the model Tax-free ea 'b avail abJ.e at the

btl!,ir.ni •• g of the development period Net revenue from the young apple and

asparagus crops

idthdrawals of tax-free cash

97 97 98 98 101 101 102 103 105

107 107 107

108

110 110 110 . 112

113

114

115

115 117

119

122

124 124 125

126

127

(9)

4,3,6.5

Tax-deductible overhead costs

128 4. 3.6.6

Total tcix-deductible expenditures

129

4. 3.6.7

Taxation limits

129

4. 3. 6.8

Summary of cash and taxation restraints

131 4. 3. 7

Objective function accounting restraints

131

The i cti vi ties

4 . 4.1 4. 4 . 2 4. 4. 3 4. 4.3 . 1 4. 4. 3.2 4 . 4. 3 . 3.

4 . 4. 3 . 4 4. 4. 3. 5 4 . 4 . 3 . 6 4. 4. 3.7 4. 4. 3 . 8 4. 4.3.9 4. 4 . 3 , 10 4. 4 . 4 4. 4. 4.1 4. 4. 4 ..

2

4. 4 . 5 4. 4. 5.1 4. 4. 5 . 2 4. 4. 6 4. 4. 6. 1 4 . 4 . 6 . 2 4. 4 . 6. 3 4. 4. 6. 4 4 . 4. 7 4. 4 . 8 4. 4 . 8. 1 4. 4 . 8. 2 4. 4 . 9 4. 4 . 10

Introduction

Intercropping activities Annual cropping activities Tomato

Green bean Beetroot Potato

Pea Carrot

Broad bean-kumara Kumara

Mangold Ryegrass

Existing perennial plantings Old as:i;;aragus

Old peach

New plantings of perennials .Asparagus

Apple

Land transfer activities Annual cropl and transfer Asparagus land transfer Peach land transfer Fallow

hCtivities to hire labour

Taxation and tax-deductible expenditures Taxation transfer activities

Tax-deductions transfer Bank activities

Final tax-free cash and final assets Input-Output Coefficients

131

132

133

134

135

136

137

138

139

(10)

4. 6 4. 7 4 . 8

4 . 5. 1 4. 5. 2 4. 5.3 4. 5 . 4 4. 5. 5 4. 5 . 6 4. 5 . 7 4 . 5. 7 . 1 4. 5. 7 . 2 4. 5. 8 4. 5. 8 . 1 4. 5. 8. 2

Introduction Land restraints Labour re~troints

Process era~ reotralnts Fresh market era~ restraints Rotaticn re~triints

Cash &nd taxation reatr~i~t3

Gener~l de~cri~ticn of coefficients Derivation of margin~l t~x r~tts

Objective function accounting reatr~ints General descriftion of coefficients Der:vation of asset values

4. 5. 8. 2 . 1

Introduction

4. 5. 8 . 2.2

The procedur e adofted

4. 5 . 8.2 . 3

Optimum re~lacement times

4. 5 . 8 . 2. 4

Calculation of asset values The Objective Function

'I'he Basic Natrix The .:iolution

.• para.me Lric solution rlctivity levels: ~lan

4

139 140 142 143 145 145 147 147 149 150 150 152 152 153 153 155 156 158 158 158 162 4.8 . 1

4. 8. 2 4. 8. 2 . 1 4. 8.2 . 2

Intercro~~ed and annual cropping activities

162

~erennial crops and land transfer

activities

163

4. 8. 2. 3 4. 8. 2. 4 4 . 8. 3 4 . 8. 4 4 . 8. 5 4 . 8 . 5. 1 4 . 8 . 5 . 2 4 . 8 . 5 . 3 4 . 8 . 5 . 4 4. 8 . 5 . 5 4. 8 . 6

Activities to hire labour Cash flows nd t~xation

Value of the objective function: Plan

4

Resource~ in dis~os&l: ~lan 4 Value of resources: Plan 4 Introduction

Annual cropland restraints Labour restraints

Process ~nd fresh market crop restraints Tax-free cash restraints

Opportunity costs of growing excluded crops: Plan

4

Effect of Varying the Length of the Pla~ning Horizon

Discussi on on the Programming Results

164 165 168 168

170 170 171 171

172 173

174

176

177

(11)

4.10.1 4.10.2 4.10.3

CHJ.f'Tl:.R 5

Physical plans and problems with changed contracts

Resource use and disposal levels

Problems associated with the variability of input-output coefficients

Value of resources Summary

~U,;'i.DR""TIC

I -_

OGRA.i',1NING

.,rD

PROFIT K,.XIMI.::i.~.TI01·

Introduction

The Ap~roach ~dopted The Restraints

5.3.1 5.3.1.1 5.3.1.2 5.3.1.3 5.3.2 5.3.3 5.3.4

Glasshouse restraints

Propagating-house (restraints R1-R13) Growing-house (restraints R14-R26) Shade-house (restraints

R27-R36)

Labour (restraints R37-R41) Land (restraint R42)

Summary of resource supplies on the hypothetical nursery

The J.cti vi ties

5 .

4.1 5.4.2 5.4.3 5.4.4 5.4.5 5.4.6 5 .. 4.7 5.4.8 5 .. 4.9 5.4.10 5.4.11 5 .. 4.12 5.4.13 5.4.14

5.4.15 5.4.16 5.4.17

Telopea speciosissima (P1) Acacia baileyana (P2)

Passiflora 'Crackerjack' (P3) Banksia grandis (P4)

Photinia robusta (P5) Eucalyptus ficifolia (P6) Stachyurus praecox (P7)

Cistus purpureus 'Brilliancy' (P8) Protea cynaroides (P9)

Tibouchina grandiflora (P10) Azalea indica ¹Salmonea' (P11) Viburnum japonicum (P12)

Rhododendron 'Christmas Cheer' (P13) Weigela florida variegata (P14) and Forsythia 'Karlsax' (:f!5)

Azalea occidentalis (P16) Magnolia stellata (P17)

Callicarpa dichotoma (P18) and Hypericum 'Hi dcote Gold' (P19)

177 179

183 183 185

186 186

186 187 188

189

190 190 191 191

191 192 192 192 193 193 193 193 194 194

194

195 195 195

196

(12)

5. 6

5.7

5.9

Input-Output Coefficients 5. 5.1

5.5.2 5.5.3 5.5.4 5.5.5

Problems of multi-period production Glasshouse restraints

Labour restr&ints Land restr&int

Dominated restraints

Matrix of ~ctivity Resource Requirements The Objective Function

5.7.1 5.7.2 5.7.3 5.7.4 5.7.5

Introduction

Estimation of the demand functions Vari.able costs

Total net revenue objective functi on Overhead costs

The Solution

5.8.1 Introduction

5.8.2 Comparison of the optimum plan and the nurseryman's plan

5.8.2.1 Production levels ~nd prices 5.8.2.2 Comparison of net revenue

5.8.2.3 Comparison of resource requirements 5.8.2.3.1 Glasshouse restraints

5.8.2.3.2 Labour and land restraints 5.8.3 Resources in disposal 5.8.4

5.8 . 5

Value of resources

The cost of including non-basic activities i n the optimum plan Comments on the ~uadratic Programming Model

and Results

5.9.1 Extension of the model to represent actual situations

Incorporation of demand cross-effects into the quadratic programme

Problems associated with the demand curves

Shadow prices and resource disposal levels

CHAI-TER 6 RISK FROGRAHLING 1.ND FRESH VEGETABLE PRODUCTION

6 . 1 6.2

Introduction The Restraints

6 . 2.1

6.2.2

Land

Labour availability

196 196

198

200 201 201 203 203 203 205 208 209 209 209 210 210 213 213 213 216

216

216 217

218

218 219 220

222

223 223 224

(13)

6 . 3

6. 4 6 . 5

6.6 6. 7

6 . 2. 3

_Rotations _~nd cropping limits The ilcti vi ties

6 . 3 . 1 6 . 3 . 2 6.3 . 3 6 . 3 . 4 6 . 3 . 5 6. 3 . 5.1 6 . 3 . 5.2 6. 3 . 6 6 . 3. 7

Production on freehold and leased l and

$pring carrot and parsnip Crown .i1w.upkin

Bu ttercui pull:pkin .::;_nd butt ernu t pumpkin Brassica activities

Winter c2uliflower and Jinter cabbage Spring cauliflower and Spring cabbage ,Vint er lettuce

Spring lettuce In.i1ut-Output Coefficients The Objective Function

6 . 5 . 1 6. 5 . 2 6 . 5 . 3 6 . 5.5 6 . 5 . 5.1 6 . 5 . 5.2 6.5.5 . 3 6 . 5 . 6

Introduction

Activity prices and yields Variable costs

Activity net revenues

Net revenue variances and covariances The variance of activity net revenues The covariance of activity net revenues The variance - covariance matrix

Overhead costs

Construction of the Initial Risk Programming Mat~ix

The Haximum Risk Solution

6. 7 . 2 . 3 6. 7. 3 6 . 7. 4

Introduction

Com.i1arison of the maximum risk solution with the grower's plan

Comparison of activity levels

Expected net revenue and net revenue variance

Comparison of resource requirements Value of resources

Marginal opportunity costs

q. 8 Summary CHAPTER 7

of the Risk Programming Model

SUMMARY OF R:SSULTS :1.ND COMMENTS ON

NATHEMATIC.1-1.L PROGRAMMING IN HORTICULTUHE Introduction

The Linear Programming Applications

225 227 22?

227 227 227 227 227

228

228 228

230 230 230 233 233 234 234 236 237 237

238 239 239

239 239 240

242

242 244

245

247

(14)

The Quadratic Programming Applications The Fotential of Mathematical Frogramming

in the New Zealand Horticultural Advisory Service

7 . 4. 1

The general use of programming techniques

7. 4. 2

The use of farm records

7. 4. 3

The role of market intelligence

7 . 5

Conclusions

A~l-ENDIX A D,\.TA l<ELJ.TING TO THE INTERT.1:,K1.·CR;..L LIN.2.,'...R FROGRi<_t,Tivit. OF CH.i-.FTr.R 4

A.1 Frice, Yield and Variable Cost Estimates for Annual Crops

A.2 Price, Yield and Variable Cost Estimates for Perennial Crops and their Optimum Replacement

A.2.1 Apple

A . 2. 2

,'.i.sparagus A.2.3 Peach

A.3 Part of the Basic Matrix

1u .t'E~DIX B D;..T_-1. OF TH.L'., R:i::SK rHOGR1-J,frlING HGD:C:L OF CH;,.t:-T.2:R 6

B.1 Description of the Data

249

250 250 251 252 253

254 254

257

258

261

263

(15)

Table

2.1 3.1 3.2 3.3 3.4 3.5 3.6 3.7 3.8 3.9 3.10 3.11 3.12 3.13 3.14 3.15 3.16 3.17 3.18 3.19 3.20

3.24 3.25 3.26 3.27 3.28 3.29 3.30

LIST OF TABLES

Initial Simplex Tableau for Quadratic Programming Labour Restraints and Supply

Cropping Limit Restraints Price and Yield Assumptions Variable Costs

Gross Margins

Variable Costs - Rhubarb (P6) Present Value of Rhubarb (P6) Variable Costs - Soleil d'Ors (P7) Present Value of Soleil d'Ors (P7) Overhead Costs

Labour Input - Lettuce Activity (P8) The Basic Matrix

The Cropping Programme

Comparison of Activity Levels and Farm Profits Between the Optimum and the Grower's Plan Gross Margin Stability Limits

Land in Disposal Labour in Disposal Land Shadow Prices

Cropping Limit Shadow Prices

The Parametric Solution - Activity Levels and Farm Profits

The Parametric Solution - Value of Scarce Resources The Adopted Cropping Programm~

Comparison of Activity Levels and Farm Profits Between the Adopted and the Grower's Plan

Land Requirements of the Adopted and the Grower's Plan Labour Requirements of the Adopted and the Grower's Plan Gross Margin Stability Limits - Adopted Plan

Price Limits - Adopted Plan Yield Limits - Adopted Plan Land in Disposal - Adopted Plan Labour in Disposal - Adopted Plan

Page

23 41 43 51 53 54 55 56 57 58 60

64 67

69 70 72 73 74 75

76

80 83

86

87

89 90 92 93

94

95

96

(16)

3.31 4.1 4.2 4.3 4.4 4.5 4.6 4.7 4.8 4.9

4.10 4.11

4.12 4.13 4.14 4.15 4.16 4.17 4.18 4.19 4.20

4.21

4.22 4.23 4.24

4.25

4.26 4.27 4.28 4.29

4.30

Impact of Taxation on Increased Profits Schematic Representation of the Basic Matrix Process Crop Contracts

Land Restraints

Labour Requirements of Maintenance Work and the Young Apple and Asparagus Crops

Labour Restraints

Process Crop Restraints Fresh Market Crop Restraints Rotation Restraints

Tax-Deductible Overhead Costs Cash and Taxation Restraints

Objective Function Accounting Restraints Land: Input-Output Coefficients

Labour: Input-Output Coefficients

Rotation Restraints: Input-Output Coefficients

Cash and Taxation Restraints: Input-Output Coefficients Marginal Tax Rates

Objective Function Accounting Restraints:

Input-Output Coefficients Asset Values of Perennial Crops The Objective Function

Price Limits of the Final Assets Activity

Crop Activity Levels Which Vary in the Parametric Solution

Values of the Objective Function in the Parametric Solution

Intercropped and Annual Cropping Activities - Plan 4 Perennial Crops and Land Transfer Activities - Plan

4

Labour to be Hired - Plan

4

Cash Flows and Taxation - Plan 4 Resources in Disposal - Plan 4 Labour Shadow Prices - Plan 4

Shadow Prices of Process and Market Crop Restraints - Plan 4

Marginal Opportunity Costs of Growing Non-Basic Crops - Plan 4

Labour Restraints

Labour Input-Photinia (P5)

Planting Methods and Land Requirements

100

111 112

116

120 121 121 123

124

128 130

131 141 144 146 148

150

151 156 157 159

160

161

162

163 165

166 169 172

173

175

190

199

200

(17)

5.4 5. 5 5.6

5.7

5.8 5.9

5 .11

5.12 5.13 6 .1 6.2

6.3

6.4

6 . 5 6 . 6

6.7

6.8 6.9

6 .10

6.11 6 .12

6 .13

6 . 14

A.1

A.2 A.3 A . 4 A .5 A, 6 A.7 A, 8

B.1 B.2

Activity Resource Requirements and Resource Supplies The Demand (Average rtevenue) Functions

Variable Costs

Output and Prices for the Optimum and the Nurseryman's Plan

Fropagating-House Requirements of the Optimum and the Nurseryman's Plan

Growing-House Requirements of the Optimum and the Nurseryman's 1-lan

Shade-House Requirements of the Optimum and the Nurseryman's Plan

Land and Labour Requirements of the Optimum and the Nurseryman's Plan

Value of Resources

Marginal Opportuni ty Costs Labour Restraints and Supplies Cropping Restraints

Activity Resource Requirements and Resource Supplies Wholesale I-rice and Quantity Sold - Crown Pumpkin Prices, Yields and Gross Revenue - Crown Pumpkin Net Revenue - Crown Fumpkin

Activity Net Revenues

Variance of rictivity Net Revenues Overhead Costs

Comparison of Activity Levels Between the Maximum Risk and the Grower's Plan

Expected Net Revenue

Resource Requirements of the Maximum Risk and the Grower's flan

Value of Resources

!-1.arginal Opportunity Costs Gross Revenue

Variable Costs Revenue, Costs Revenue, Costs Revenue, Costs Sub-Matrix a Sub-Matrix g Sub-Matrix h

from Annual Crops of Annual Crops

and Optimum Replacement:

and Optimum Replacement: and Optimum Replacement:

Quantities Sold, Acreages and Yields

Apples Asparagus Peaches

Average Net Wholesale }'rices, Yields and Gross Revenues

202 206 207

211 213 214 215

215

217 218 225 226

229

231 232 233 234

235

237

240

241

243

244

255 256 259

260

26 4

265

266

268

(18)

B . 3 B . 4

Figure 2.1 2.2 3.1

3 . 2

Variable Costs

The Net Revenue Variance - Covariance Matrix

LIST C.f FIGURES

hn E - V Indifference Jystem

Expected Income as a Function of Income Variance Activity Land Requirements

The Farametric Solution

270 271

Page

29

38

81

Applications of mathematical programming on four New Zealand horticultural holdings : a thesis presented in partial fulfilment of the requirements for the degree of Master of Horticultural Science in Massey University

Copyright is owned by the Author of the thesis. Permission is given for

APPLICATIONS OF MATHEMATICAL PROGRAMMING

CONTENTS

CHAFT:C:R 3

Callicarpa dichotoma (P18) and Hypericum 'Hi dcote Gold' (P19)

CHAI-TER 6 RISK FROGRAHLING 1.ND FRESH VEGETABLE PRODUCTION

q. 8 Summary CHAPTER 7

SUMMARY OF R:SSULTS :1.ND COMMENTS ON

LIST OF TABLES