N10,046.70 and N6,952.11 with the L-, Z- and H- models respectively. For the N1,000.00 labour rate, the corresponding annual ridger machinery cost was N7,222.75, N10.966.73 and N7,229.94 with the L-, Z- and H- models respectively. The obtained results showed that labour cost affect the annual ridger machinery cost predicted by the tillage machinery models and the ridger sizes predicted by the L- model.
Figure 4.9: Selected minimum-cost ridger width (A) and annual ridger machinery cost per hectare (B) for varying labour rates
Generally the tillage machine width predicted by the L- model increased with increasing labour rate. In this way the labour use hours will decrease thereby limiting the increase in the labour cost that would have otherwise resulted from the labour rate increase. Increased machine size and cost will however lead to increased machine fixed cost, fuel consumption and required tractor size. This agrees with the findings of Srivastava et al (2006) that increasing the field machine size inreases the machinery cost but reduces labour cost. The Z-and H- models could not respond to the change in the labour rate. This can be attributed to the lack of consideration of the labour cost in the development of the Z- and H- models. The machinery cost per hectare corresponding to the macine widths obtained with each of the 3 models increased with increasing labour rate. The Z- model cost was the highest at each labour rate for all the tillage implements. The L- model gave the lowest cost for all the machinery at the N1,000.00 labour rate and for the plough machinery at all the labour rates.
The H- model cost was the lowest for the harrow and ridger machinery at the lower rate.
The effect of the change in the arbitrary prior field capacity value on the selectd machine width was reported in this subsection. The effect was presented and discussed for the plough, harrow and ridger machinery widths predicted for a fixed farm size of 420 ha.
I) Effect of chosen prior field capacity change on predicted plough width and machinery cost:
The predicted minimum-cost width and the corresponding annual plough machinery cost per hectare for changing prior field capacity for a 420 ha farm is shown in Table 4.9. The minimum-cost plough width is also shown in Figure 4.10A and the annual plough machinery Table 4.9: Predicted plough widths and machinery costs for varying chosen prior capacities
Prior Capacity
used (ha/hr)
Equivalent Working Width w
(m)
Selected Plough Width w (m)
Annual Machinery Cost per Hectare (N)
wL wZ wH ACL ACZ ACH
0.2067 0.6 1.8059 0.8650 0.9716 6392.60 7213.28 7001.08 0.3101 0.9 1.8059 0.8650 1.2738 6392.60 7213.28 6634.52 0.4134 1.2 1.8059 0.8650 1.5438 6392.60 7213.28 6471.26 0.5168 1.5 1.8059 0.8650 1.7923 6392.60 7213.28 6395.31
cost per hectare in Figure 4.10B. A plough width of 0.9716 m was predicted by the H- model for 0.2067 ha/hr prior plough capacity input. For 0.3101 ha/hr, 0.4134 ha/hr and 0.5168 ha/hr prior capacities input the selected plough widths were 1.2738 m, 1.5438 m and 1.7923 m respectively with the same H- model. These plough capacities corresponded to plough working widths of 0.6 m, 0.9 m, 1.2 m and 1.5 m respectively at the plough speed of 5.3 km/hr and field efficiency of 0.65 used. The L- and Z- models-predicted plough widths were 1.8059 m and 0.8650 m respectively, and remained unchanged for changes in prior plough capacity input.
The incurred plough machinery cost per hectare was N7,001.08, N6,634.52, N6,471.26, and N6,395.31 for the widths predicted with the H- model for the listed prior capacities in the same order. The cost per hectare was N6,392.60 based on the L- model and N7,213.28 based on the Z- model for the 0.2067 ha/hr prior capacity and remained unchanged for the other capacities.
107
0.2067 0.3101 0.4134 0.5168
0.0 0.4 0.8 1.2 1.6 2.0
wL wZ wH
Prior Capacity Used (ha/hr)
Minimum-cost Plough Width w (m)
0.2067 0.3101 0.4134 0.5168
6000.0 6500.0 7000.0 7500.0
ACL ACZ
ACH
Prior Capacity Used (ha/hr)
Plough Machinery Cost per Hectare (N/ha)
(A) (B)
Figure 4.10: Selected minimum-cost plough width (A) and annual plough machinery cost per hectare (B) for varying chosen prior capacities
II) Effect of chosen prior field capacity change on predicted harrow width and machinery cost: The predicted annual harrow machinery cost per hectare and the minimum-cost width obtained when the labour rate per hectare changes for a 420 ha farm is shown in Table 4.10.
The minimum-cost harrow width is also shown in Figure 4.11A and the annual harrow machinerycost per hectare in Figure 4.11B. A harrow width of 1.4016 m was predicted by the H- model for 0.5741 ha/hr prior harrow capacity input. For 0.7507 ha/hr, 0.9274 ha/hr and 1.1040 ha/hr prior capacities input the selected harrow widths were 1.6774 m, 1.9327 m Table 4.10: Predicted harrow widths and machinery costs for varying chosen prior capacities
Prior Capacity
used (ha/hr)
Equivalent Working Width w
(m)
Selected Harrow Width w (m)
Annual Machinery Cost per Hectare (N)
wL wZ wH ACL ACZ ACH
0.5741 1.3 1.5649 0.7089 1.4016 4481.92 5247.12 4512.60 0.7507 1.7 1.5649 0.7089 1.6774 4481.92 5247.12 4474.15 0.9274 2.1 1.5649 0.7089 1.9327 4481.92 5247.12 4485.85 1.1040 2.5 1.5649 0.7089 2.1726 4481.92 5247.12 4523.60
and 2.1726 m respectively with the same H- model. These harrow capacities corresponded to harrow working widths of 1.3 m, 1.7 m, 2.1 m and 2.5 m respectively at the harrow speed of 6.4 km/hr and field efficiency of 0.69 used. The L- and Z- models-predicted harrow widths were 1.5649 m and 0.7089 m respectively, and remained unchanged for changes in prior harrow capacity input.
The incurred harrow machinery cost per hectare was N4,512.60, N4,474.15, N4,485.85, and N4,523.60 for the widths predicted with the H- model for the listed prior capacities in the
108
0.5741 0.7507 0.9274 1.1040
0.0 0.5 1.0 1.5 2.0 2.5
wL wZ wH
Prior Capacity Used (ha/hr)
Minimum-cost Harrow Width w (m)
0.5741 0.7507 0.9274 1.1040
4000.0 4500.0 5000.0 5500.0
ACL ACZ ACH
Prior Capacity Used (ha/hr)
Harrow Machinery Cost per Hectare (N'000/ha)
(A) (B)
Figure 4.11: Selected minimum-cost harrow width (A) and annual harrow machinery cost per hectare (B) for varying chosen capacities
same order. The cost per hectare was N4,481.92 based on the L- model and N5,247.12 based on the Z- model for the 0.5741 ha/hr prior capacity and remained unchanged for the other capacities.
III) Effect of chosen prior field capacity change on predicted ridger width and machinery cost: The predicted annual ridger machinery cost per hectare and the minimum-cost width obtained when the labour rate per hectare changes for a 420 ha farm is shown in Table 4.11.
The minimum-cost ridger width is also shown in Figure 4.11A and the annual ridger machinery cost per hectare in Figure 4.11B. A ridger width of 1.1449 m was predicted by the H- model for 0.2673 ha/hr prior ridger capacity input. For 0.5346 ha/hr, 0.8019 ha/hr and 1.0692 ha/hr prior capacities input the selected ridger widths were 1.8178 m, 2.3826 m and 2.8869 m respectively with the same H- model. These ridger capacities corresponded to ridger working widths of 0.9 m, 1.8 m, 2.7 m and 3.6 m respectively at the ridger speed of4.5 km/hr and field efficiency of 0.66 used. The L- and Z- models-predicted ridger widths were 1.5847 m and 0.5490 m respectively, and remained unchanged for changes in prior ridger capacity input.
Table 4.11: Predicted ridger widths and machinery costs for varying chosen prior capacities Prior
Capacity used (ha/hr)
Equivalent Working Width w
(m)
Selected Ridger Width w (m)
Annual Machinery Cost per Hectare (N)
wL wZ wH ACL ACZ ACH
0.2673 0.9 1.5847 0.5490 1.1449 6764.97 9126.67 7147.54 0.5346 1.8 1.5847 0.5490 1.8178 6764.97 9126.67 6674.28 0.8019 2.7 1.5847 0.5490 2.3826 6764.97 9126.67 6609.31 1.0692 3.6 1.5847 0.5490 2.8869 6764.97 9126.67 6652.93
The incurred ridger machinery cost per hectare was N7,147.54, N6,674.28, N6,609.31 and N6,652.93 for the widths predicted with the H- model for the listed prior capacities in the same order. The cost per hectare was N6,764.97 based on the L- model and N9,126.67 based on the Z- model for the 0.2673 ha/hr prior capacity and remained unchanged for the other capacities.
Figure 4.12: Selected minimum-cost ridger width (A) and annual ridger machinery cost per hectare (B) for varying chosen capacities
Generally the obtained results showed that the chosen prior tillage capacity affected the predicted tillage width for the H- model and that the choice of a proper prior capacity is needed to realize cost minimization with this model. The choice of a prior tillage capacity input was not needed for the L- and Z- models developed in the study. This shows that the developed models were more objective and less dependent on the user’s experience.