Ngā Tauira Pātai e Matapaki ana i te Whakamahinga o ngā Taurite i roto i te Marae o te Ōhanga me te Pakihi
Pendahuluan
He ariā matua ngā taupū i roto i te tātaitai, ā, he maha ngā whakamahinga i roto i ngā momo mara, tae atu ki te ōhanga me te pakihi. I roto i tēnei horopaki, he maha ngā whakamahinga o ngā taupū hei tātari i te hua katoa, te utu, te moni whiwhi, me ngā mahi kai me te whakaputa. Mā te mārama ki te whakamahinga o ngā taupū i roto i te ōhanga me te pakihi, ehara i te mea ka āwhina noa i te whakaoti rapanga hangarau engari ka whakarato hoki i ngā māramatanga hohonu ake ki ngā hihiri mākete, te whakatau kaupapa, me te whakamahere rautaki.
Ngā Taupānga Whakauru i roto i te Ōhanga me te Pakihi
1. Tātaihia te Tapeke Moni Whiwhi
Hei tatau i te tapeke o ngā moni whiwhi, me tāpirihia ngā moni whiwhi iti mai i te hokonga o ngā waeine takitahi o tētahi hua. Mena ka rerekē te utu o tētahi hua i runga i te rahinga i hokona, me whakauru te mahi utu-rahinga hei whakatau i te tapeke o ngā moni whiwhi.
Tauira raruraru:
Me kī ko te utu \( p \) o tētahi taonga e whakawhirinaki ana ki te nui o te hua \( q \) i hokona, e homai ana e te mahi e whai ake nei:
\[ p(q) = 100 – 2q \]
Tātaihia te tapeke o ngā moni whiwhi mēnā ka hokona ngā waeine taonga e 10.
Otinga:
Ko te moni whiwhi katoa \( R \) te tauwehenga o te utu ki runga i te rahinga mai i te 0 ki te \( Q \) waeine.
\[ R = \int_{0}^{Q} p(q) \, dq \]
Me \( p(q) = 100 – 2q \) me \( Q = 10 \):
\[ R = \int_{0}^{10} (100 – 2q) \, dq \]
Nā, ka tatauhia e mātou te taupū:
\[ R = \left[ 100q – q^2 \right]_{0}^{10} \]
Arotakehia ngā rohe o te taupū:
\[ R = \left( 100 \cdot 10 – 10^2 \right) – \left( 100 \cdot 0 – 0^2 \right) \]
\[ = 1000 – 100 \]
\[ = 900 \]
Nō reira, ko te tapeke moni whiwhi mēnā ka hokona ngā waeine taonga e 10 he 900.
2. Tātaihia te Utu Katoa
He tino whai hua te whakamahinga o ngā taunga whakauru hei tatau i ngā utu whakaputa katoa, inā koa kāore ngā utu taha e pumau, ā, e whakawhirinaki ana ki te rahinga i whakaputaina. Ka taea te whakaahua i ngā utu taha hei pānga o ngā utu katoa, ā, hei kimi i ngā utu katoa me whakauru tātou.
Tauira raruraru:
Mena ka homai te utu taha \( MC \) mō te whakaputa \( q \) i ngā waeine o tētahi taonga e:
MC(q) = 50 + 3q^2
Tātaihia te utu katoa mēnā e 5 ngā waeine taonga ka hangaia, me te whakaaro ko ngā utu pumau \( C \) he 200.
Otinga:
Ko te utu katoa \( TC \) te taupū o te utu taha me te utu pumau:
\[ TC = \int_{0}^{Q} MC(q) \, dq + C \]
Me \( MC(q) = 50 + 3q^2 \) me \( Q = 5 \):
\[ TC = \int_{0}^{5} (50 + 3q^2) \, dq + 200 \]
Ka tatauhia e mātou te taupū:
\[ TC = \left[ 50q + q^3 \right]_{0}^{5} + 200 \]
Arotakehia ngā rohe o te taupū:
TC = \left( 50 \cdot 5 + 5^3 \right) – \left( 50 \cdot 0 + 0^3 \right) + 200 \]
\[ = \maui( 250 + 125 \matau) + 200 \]
\[ = 375 + 200 \]
\[ = 575 \]
Nō reira, ko te tapeke o te utu hei whakaputa i ngā waeine taonga e 5 he 575.
3. Te Tātai i te Whakamahinga Rauemi
Ka whakamahia hoki ngā taunga whakauru hei tatau i te whakapaunga katoa, te whakamahinga rānei o tētahi rauemi i roto i tētahi wā kua whakaritea. He mea nui tēnei i roto i ngā horopaki pakihi e pā ana ki ngā rauemi pēnei i te pūngao, ngā rauemi, ngā tāngata rānei.
Tauira raruraru:
Ko te tere whakapaunga pūngao o ia rā \( E \) i roto i tētahi wheketere e whai ana i te mahi taupūpū e whai ake nei:
\[ E(t) = 10e^{0.1t} \]
Tātaihia te tapeke o te pūngao e pau ana mō ngā rā 10.
Otinga:
Ko te tapeke o te whakapaunga pūngao \( C \) i roto i te wā [0, T] ko te taupū o aua reiti whakapaunga pūngao:
\[ C = \int_{0}^{T} E(t) \, dt \]
Me \( E(t) = 10e^{0.1t} \) me \( T = 10 \):
\[ C = \int_{0}^{10} 10e^{0.1t} \, dt \]
Hei tatau i te taupū, ka taea e tātou te whakamahi i te tikanga whakakapinga:
Me \( u = 0.1t \), kātahi ka \( du = 0.1 \, dt \), me \( dt = \frac{du}{0.1} \),
\[ C = \int_{0}^{1} 10e^{u} \frac{du}{0.1} \]
\[ = 100 \int_{0}^{1} e^{u} \, du \]
\[ = 100 \left[ e^{u} \right]_{0}^{1} \]
Arotakehia ngā rohe o te taupū:
\[ C = 100 \left( e^{1} – e^{0} \right) \]
\[ = 100 \left( e – 1 \right) \]
Me \( e \tata ki te 2.718 \):
\[ C \tata ki te 100 (2.718 – 1) \]
\[ = 100 \whakareatia ki te 1.718 \]
\[ = 171.8 \]
Nō reira, ko te tapeke o te pūngao e pau ana mō ngā rā 10 he 171.8 waeine pūngao.
Whakamutunga
He mea nui te ariā o ngā taunga whakauru i roto i te ōhanga me te pakihi, nā te mea ka taea e ngā kaitātari me ngā kaiwhakatau te tatau me te matapae i ngā taurangi nui pēnei i te moni whiwhi, ngā utu, me te kai. Mā te mārama ki te whakamahi i ngā taunga whakauru i roto i ēnei horopaki ka taea te whakarato i tētahi painga whakataetae me te māramatanga pai ake ki ngā mahi pakihi. Ko te tumanako, mā ēnei tauira raruraru koe e āwhina ki te mārama ki ngā tono mahi a ngā taunga whakauru i roto i te ōhanga me te pakihi.
