To enhance crop yields, narrowing the gap between actual and achievable yields is crucial. One approach involves identifying yield-limiting factors and their optimal levels. Boundary line analysis (BLA), a statistical method, quantifies yield response to environmental or managerial factors while accounting for variable factors. In 2020, a study surveyed 180 spring sugar beet farms in Iran. The findings revealed a 50.7 % yield gap (11.13 t ha -1 ) between farmers' average sugar yield (10.84 t ha -1 ) and potential yield (21.97 t ha -1 ). BLA implicated low plant density, soil organic content, lack of potassium (K)-containing fertilizers, and non-adherence to crop rotation principles in 81.3 %, 75.5 %, 53.4 %, and 51.1 % of farms, respectively. Optimal levels were estimated at 9.5 plants m -1 , 1.15 % soil organic content, 100 kg ha -1 K fertilization rate, and 5-9.8 as the rotation numerical value. Other limiting factors included time from cultivation to thinning and sowing date. The optimal minimum time between planting and thinning stood at 38 days, with the latest sowing date estimated at 94 Julian days (May 5). Achieving attainable yield necessitates limiting root exposure to 4.9 days, keeping disease damage below 15.3 %, and increasing irrigation frequency to over 10 times. In the short term, increasing plant density to optimal levels, promoting K fertilizer use, and adjusting thinning and sowing dates can significantly boost sugar yield per unit area.

Aim: To determine the optimum level of phosphorus for higher yield and phosphorus uptake by groundnut at different planting densities. Methodology: A field experiment was laid out in randomized block design with factorial concept during Rabi seaon 2019-20 to study the phosphorus uptake by groundnut under high density plantation (22.5 x 10 cm - 4.44 lakh ha(-1) ; 20 x 7.5 cm - 6.66 lakh ha(-1) ; 22.5 x 5 cm - 8.88 lakh ha(-1) with graded levels of phosphorus (25, 37.5, 50 and 62.5 kg P2O5 ha(-1) ). Results: The present study revealed that 4.44 lakh ha registered lower phosphorus uptake and application of 62.5 kg P2O5 ha recorded a higher uptake of phosphorus and soil available nitrogen, phosphorus, and potassium. Interaction was significant only in influencing pod yield. Higher pod yield was recorded in the population density of 4.44 lakh ha applied along with 50 kg P2O5 ha , followed by 6.66 lakh ha applied with 62.5 kg P O ha(-1) . Interpretation: The results indicate that for better nutrient uptake and higher pod yield of groundnut, farmers should prefer a planting density of 6.66 lakh ha(-1) with an application of 62.5 kg P2O5 ha(-1) .