ASRB NET - Agricultural Statistics (and Computer Application / Bioinformatics) · India · Agricultural Scientists Recruitment Board (ICAR)
Original practice questions written to the published syllabus · not past papersThe optimisation theory statisticians use: linear programming with simplex and duality, transportation and assignment, integer and goal programming for farm and crop planning, non-linear optimisation with Kuhn-Tucker conditions, and the numerical optimisers inside likelihood estimation. The Agribusiness track teaches operations research for managers; this goes to the theory.
In the exams: AICE-JRF Ag Stat Unit 2 'linear programming: formulation, graphical, simplex, duality, transportation and assignment' (heavy); UPSC ISS Statistics III operations research (heavy, reported); ASRB NET Ag Stat (present)
ASRB NET / ARS Agricultural Statistics
Formulating farm-planning and ration problems, interpreting shadow prices and sensitivity, goal and risk programming in farm planning.
How our questions for ASRB NET spread across the units of Optimization Techniques for Statisticians. Difficulty: 14 easy, 36 medium, 9 hard.
| Linear programming: formulation and graphical solution | 9 | |
| Quadratic programming and risk programming (MOTAD) | 9 | |
| Duality and sensitivity analysis | 8 | |
| Transportation and assignment problems | 8 | |
| Goal programming for multi-objective farm planning | 8 | |
| Simplex method, Big-M and two-phase methods | 6 | |
| Integer programming: branch and bound | 4 | |
| Dynamic programming | 4 | |
| Numerical optimisation: gradient, Newton and quasi-Newton methods | 2 | |
| Non-linear programming: Lagrange multipliers and Kuhn-Tucker conditions | 1 |
Choose an answer, then open the working. Each explanation says why the right answer is right and why the others are not.
Which assumption of LP is violated when fractional animals cannot be kept?
D. Divisibility
Divisibility allows fractional activity levels; integer requirements need integer programming.
Further reading: Taha, Operations Research: An Introduction; Hazell and Norton, Mathematical Programming for Economic Analysis in Agriculture; Nocedal and Wright, Numerical Optimization
Which variable converts a ≤ constraint into an equation in the simplex method?
C. A slack variable
Slack = unused resource, added to ≤ constraints; surplus is subtracted from ≥ constraints.
Further reading: Taha, Operations Research: An Introduction; Hazell and Norton, Mathematical Programming for Economic Analysis in Agriculture; Nocedal and Wright, Numerical Optimization
Land has a shadow price of 20 thousand currency units per hectare. Renting more land costs 15 per hectare. What should the farmer do?
C. Rent more, within the RHS range
Each extra hectare adds 20 at a cost of 15, but only within the range over which the shadow price stays valid.
Further reading: Taha, Operations Research: An Introduction; Hazell and Norton, Mathematical Programming for Economic Analysis in Agriculture; Nocedal and Wright, Numerical Optimization
A balanced transportation problem has 3 sources and 4 destinations. How many basic (allocated) cells does a non-degenerate basic solution have?
B. 6
m + n − 1 = 3 + 4 − 1 = 6.
Further reading: Taha, Operations Research: An Introduction; Hazell and Norton, Mathematical Programming for Economic Analysis in Agriculture; Nocedal and Wright, Numerical Optimization
An assignment problem maximises yields of varieties at sites. How is it converted for the Hungarian method?
B. Subtract entries from the maximum
Regret = maximum − entry turns maximisation into minimisation; negating also works but the standard device is subtraction from the maximum.
Further reading: Taha, Operations Research: An Introduction; Hazell and Norton, Mathematical Programming for Economic Analysis in Agriculture; Nocedal and Wright, Numerical Optimization
With 12 ha and a 20-day labour limit, wheat (40/ha, 2 days) and mustard (30/ha, 1 day), can an income goal of 450 be met?
A. No; the maximum is 440
Maximising 40x + 30y with x + y ≤ 12 and 2x + y ≤ 20 gives (8, 4) and 440 < 450, so the goals conflict and weights decide the compromise.
Further reading: Taha, Operations Research: An Introduction; Hazell and Norton, Mathematical Programming for Economic Analysis in Agriculture; Nocedal and Wright, Numerical Optimization
A mixed model reports non-convergence. Which cause is most common?
B. Over-parameterisation
Unidentifiable or boundary parameters make the objective flat or constrained; simplifying or reparameterising usually helps.
Further reading: Taha, Operations Research: An Introduction; Hazell and Norton, Mathematical Programming for Economic Analysis in Agriculture; Nocedal and Wright, Numerical Optimization
In the farm LP with 12 ha land and 16 labour-days, which constraints bind at the optimum (4, 8)?
D. Both land and labour
4 + 8 = 12 ha and 2 × 4 + 8 = 16 days: both resources are fully used, so both have positive shadow prices.
Further reading: Taha, Operations Research: An Introduction; Hazell and Norton, Mathematical Programming for Economic Analysis in Agriculture; Nocedal and Wright, Numerical Optimization
What is the dual of the dual of an LP?
C. The original primal
Duality is symmetric: dualising twice returns the primal.
Further reading: Taha, Operations Research: An Introduction; Hazell and Norton, Mathematical Programming for Economic Analysis in Agriculture; Nocedal and Wright, Numerical Optimization
How many possible one-to-one assignments exist for 4 tractors and 4 fields?
D. 24
n! = 4! = 24; 16 = 4² counts cells, not assignments.
Further reading: Taha, Operations Research: An Introduction; Hazell and Norton, Mathematical Programming for Economic Analysis in Agriculture; Nocedal and Wright, Numerical Optimization
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