Abstract
This study was executed to offer the basis for optimized profit from fertilizer use for sorghum yield and to determine robust crop nutrient response function and economic rate for the production of sorghum at Miesso Central Rift Valley of Ethiopia. Trails were conducted at six experimental sites, sorghum yield response to N and P fertilizers application and economically optimum rates of nitrogen (EONR) and phosphorus (EOPR) were evaluated on a vertisols within the semi-arid Miesso districts west Hararge zone of Oromia region. The nutrient rates in 2014 cropping season four levels of Nitrogen (N) alone, these levels with 20 kg·ha−1 Phosphorus (P) and without N, 69 kg·ha−1 N with three levels of P treatments including the zero control were evaluated. In 2015, cropping season similar rates of N alone, the same rate N with 20 kg·ha−1 P, 92 kg·ha−1 N with three rates of P including the zero control were evaluated. The treatments were arranged in a randomized complete block with three replications in factorial design. Nutrient responses of sorghum were determined using asymptotic quadratic plateau functions. The significantly highest nitrogen rate was 46 kg·ha−1 alone in 2014 season, which gave grain yield of 2.56 Mg·ha−1 with a maximum yield advantage of 43%. P rates in both seasons and combined (sites + seasons) were not significantly influenced sorghum yield. Nitrogen agronomic and partial factor productivity peaked at 23 kg N ha−1 but declined with increasing N rate. The EONR combined (sites + seasons) were 37, 45, 52 and 60 kg·ha−1 and for the profit to cost ratio (PCR) were 2.43, 3.65, 4.86 and 5.79 at difference cost to grain price ratios (CP) = 3.6, 2.3, 1.6 and 1.2 respectively at Miesso Ethiopia. Nitrogen application had economically profitable than P. The study concluded that the application of N at 37 or 60 kg N ha−1 to sorghum production could be economically profitable for those economically constrained farmers or economically not constrained farmers. Validation should be farther conducted on farmers’ fields for refining the results obtained.
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Claims 8
Claim · model-written summary
In 2014, 46 kg·ha−1 nitrogen gave the highest sorghum grain yield, 2.56 Mg·ha−1, with a 43% yield advantage.
Not reportedComparator
Organisms pictured · Representative pictures of the matched species, not figures from the paper.

Verbatim
e0“The significantly highest nitrogen rate was 46 kg·ha−1 alone in 2014 season, which gave grain yield of 2.56 Mg·ha−1 with a maximum yield advantage of 43%”
t0“Sorghum”
Claim · model-written summary
Phosphorus rates did not significantly influence sorghum yield across seasons and combined sites.
Not reportedComparatorDirection
Organisms pictured · Representative pictures of the matched species, not figures from the paper.

Verbatim
e0“P rates in both seasons and combined (sites + seasons) were not significantly influenced sorghum yield”
Claim · model-written summary
Nitrogen agronomic productivity peaked at 23 kg N ha−1 and declined at higher N rates.
Organisms pictured · Representative pictures of the matched species, not figures from the paper.

Verbatim
e0“Nitrogen agronomic and partial factor productivity peaked at 23 kg N ha−1 but declined with increasing N rate”
t0“Sorghum”
Claim · model-written summary
Nitrogen partial factor productivity peaked at 23 kg N ha−1 and declined at higher N rates.
Organisms pictured · Representative pictures of the matched species, not figures from the paper.

Verbatim
e0“Nitrogen agronomic and partial factor productivity peaked at 23 kg N ha−1 but declined with increasing N rate”
t0“Sorghum”
Claim · model-written summary
Across sites and seasons, economically optimal N rates ranged from 37 to 60 kg·ha−1 across price ratios.
Organisms pictured · Representative pictures of the matched species, not figures from the paper.

Verbatim
e0“The EONR combined (sites + seasons) were 37, 45, 52 and 60 kg·ha−1”
t0“Sorghum”
Claim · model-written summary
Profit to cost ratios at the respective price ratios were 2.43, 3.65, 4.86 and 5.79.
Organisms pictured · Representative pictures of the matched species, not figures from the paper.

Verbatim
e0“for the profit to cost ratio (PCR) were 2.43, 3.65, 4.86 and 5.79 at difference cost to grain price ratios (CP) = 3.6, 2.3, 1.6 and 1.2 respectively”
t0“Sorghum”
Claim · model-written summary
Nitrogen application was more economically profitable than phosphorus application.
Organisms pictured · Representative pictures of the matched species, not figures from the paper.

Verbatim
e0“Nitrogen application had economically profitable than P”
t0“Sorghum”
Claim · model-written summary
The authors concluded that applying 37 or 60 kg N ha−1 could be profitable for farmers with differing economic constraints.
- Outcome
- application of N at 37 or 60 kg N ha−1e0
Organisms pictured · Representative pictures of the matched species, not figures from the paper.

Verbatim
e0“application of N at 37 or 60 kg N ha−1 to sorghum production could be economically profitable”
e1“economically constrained farmers or economically not constrained farmers”
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