Mienzaniso yeMibvunzo Inokurukura Masisitimu Ekusaenzana Kwemitsara
Sisitimu yekusaenzana kwemutsara ibazi remasvomhu rinosanganisira hukama huripo pakati pekusaenzana kwemutsara kwakasiyana-siyana. Sisitimu iyi ine kusaenzana kuviri kana kupfuura kunoda kugadziriswa kuti pave nemhinduro inogutsa kusaenzana kwese panguva imwe chete. Kukurukurirana kwesisitimu yekusaenzana kwemutsara kunowanzoonekwa muzvidzidzo zvemasvomhu padanho repamusoro nerepamusoro, mumibvunzo yebvunzo uye mukuita kwezuva nezuva.
Masisitimu ekusaenzana kwemutsara ane mashandisirwo akawanda chaiwo, kubva pakugadzirisa zviwanikwa uye kuronga mari kusvika kuzvinhu zvinofambisa zvinhu. Kunzwisisa pfungwa idzi hakungokoshi chete pakugadzirisa matambudziko emasvomhu kuchikoro asiwo kunogadzirira vadzidzi kugadzirisa matambudziko ezuva nezuva zvine musoro uye zvinobudirira. Heano mimwe mienzaniso yematambudziko nekukurukurirana nezvemasisitimu ekusaenzana kwemutsara.
Muenzaniso Mubvunzo 1
Mubvunzo:
Sarudza seti yemhinduro yehurongwa hunotevera hwekusaenzana kwemutsara:
\[
\kutanga{zviitiko}
x + y \leq 6 \\
x – y \geq 2
\kupera{cases}
\]
Kukurukurirana:
1. Dhirowa mutsetse wemuganhu wekusaenzana kwega kwega:
Pa \(x + y \leq 6\), tinodhirowa mutsetse \(x + y = 6\):
– Kana \(x = 0\), \(y = 6\) yaburitsa poindi (0, 6).
– Kana \(y = 0\), \(x = 6\) yaburitsa poindi (6, 0).
Pa \(x – y \geq 2\), tinodhirowa mutsetse \(x – y = 2\):
– Kana \(x = 2\), \(y = 0\) yaburitsa poindi (2, 0).
– Kana \(y = -2\), \(x = 0\) yaburitsa poindi (0, -2).
2. Sarudza nzvimbo yekugara:
– Mutsetse \(x + y = 6\) unouparadzanisa kuita matunhu maviri, uye tinoongorora poindi imwe chete yekuyedza isiri pamutsetse, semuenzaniso poindi (0, 0):
\[
0 + 0 \leq 6 \quad (\text{true})
\]
Saka, nzvimbo inogutsa iri pasi kana kuruboshwe rwemutsetse \(x + y = 6\).
– Mutsetse \(x – y = 2\) unopatsanura skrini zvakare kuita matunhu maviri, uye tinoongorora poindi (0, 0):
\[
0 – 0 \geq 2 \quad (\text{false})
\]
Saka, nzvimbo inogutsa iri pamusoro kana kurudyi kwemutsetse \(x - y = 2\).
3. Sarudza nzvimbo dzinosangana matunhu maviri aya:
Mhinduro yehurongwa idunhu rinogutsa kusarongeka kwese kuri kuviri. Tinotsvaga nzvimbo inopindirana matunhu maviri inoenderana nekwakananga kusarongeka kwega kwega.
Mhedziso:
Seti yemhinduro yehurongwa hwekusaenzana kwemutsara ndiyo nzvimbo dzese dziri pakati penzvimbo mbiri dzinosangana nemamiriro \(x + y \leq 6\) uye \(x - y \geq 2\).
Muenzaniso Mubvunzo 2
Mubvunzo:
Sarudza seti yemhinduro yehurongwa hunotevera hwekusaenzana kwemutsara muchikamu chekutanga:
\[
\kutanga{zviitiko}
2x + 3y \leq 12 \\
x \geq 0 \\
y \geq 0 \\
\kupera{cases}
\]
Kukurukurirana:
1. Dhirowa mutsetse wemuganhu wekusaenzana kwega kwega:
Pa \(2x + 3y \leq 12\), tinodhirowa mutsetse \(2x + 3y = 12\):
– Kana \(x = 0\), \(y = 4\) yaburitsa poindi (0, 4).
– Kana \(y = 0\), \(x = 6\) yaburitsa poindi (6, 0).
2. Sarudza nzvimbo yekugara:
– Mutsetse \(2x + 3y = 12\) uye poindi yekuyedza (0, 0):
\[
2(0) + 3(0) \leq 12 \quad (\text{true})
\]
Saka, nzvimbo inogutsa iri pasi kana kuruboshwe rwemutsetse \(2x + 3y = 12\).
– \(x \geq 0\) uye \(y \geq 0\) zvinoratidza kuti poindi yemhinduro iri muchikamu chekutanga.
3. Sarudza nzvimbo dzinosangana matunhu maviri aya:
Mhinduro yesystem iyi inzvimbo iri muchikamu chekutanga chiri pasi kana kuruboshwe rwemutsetse \(2x + 3y = 12\).
Mhedziso:
Seti yemhinduro yehurongwa hwekusaenzana kwemutsara ndiyo mapoinzi ari muchikamu chekutanga chinogutsa \(2x + 3y \leq 12\).
Muenzaniso Mubvunzo 3
Mubvunzo:
Sarudza seti yemhinduro yehurongwa hunotevera hwekusaenzana kwemutsara:
\[
\kutanga{zviitiko}
y \geq 2x – 3 \\
y \leq -x + 1
\kupera{cases}
\]
Kukurukurirana:
1. Dhirowa mutsetse wemuganhu wekusaenzana kwega kwega:
Kune \(y \geq 2x – 3\), tinodhirowa mutsetse \(y = 2x – 3\):
– Kana \(x = 0\), \(y = -3\) yaburitsa poindi (0, -3).
– Kana \(y = 0\), \(x = 1,5\) yaburitsa poindi (1.5, 0).
Kune \(y \leq -x + 1\), tinodhirowa mutsetse \(y = -x + 1\):
– Kana \(x = 0\), \(y = 1\) yaburitsa poindi (0, 1).
– Kana \(y = 0\), \(x = 1\) yaburitsa poindi (1, 0).
2. Sarudza nzvimbo yekugara:
– Mutsetse \(y \geq 2x – 3\) unoedzwa ne point (0, 0):
\[
0 \geq 2(0) – 3 \quad (\text{true})
\]
Saka, nzvimbo inogutsa iri pamusoro kana kurudyi rwemutsetse \(2x - 3\).
– Mutsetse \(y \leq -x + 1\) unoedzwa ne point (0, 0):
\[
0 \leq -0 + 1 \quad (\text{true})
\]
Saka, nzvimbo inogutsa iri pasi kana kuruboshwe rwemutsetse \(-x + 1\).
3. Sarudza nzvimbo dzinosangana matunhu maviri aya:
Mhinduro yehurongwa idunhu rinogutsa kusarongeka kwese kuri kuviri. Tiri kutsvaga dunhu rinosangana kusarongeka kwese uku.
Mhedziso:
Seti yemhinduro yehurongwa hwekusaenzana kwemutsara ndiyo mapoinzi ari pamharadzano yedunhu anogutsa \(y \geq 2x - 3\) uye \(y \leq -x + 1\).
Nekunzwisisa maitiro ekugadzirisa masisitimu ekusaenzana kwemutsara, zvinotarisirwa kuti vadzidzi vachava nehunyanzvi hwekugadzirisa matambudziko emasvomhu nekushandisa pfungwa idzi mumamiriro ezvinhu ezuva nezuva. Tinovimba kuti, mienzaniso yematambudziko aya nehurukuro zvichabatsira vadzidzi kudzidza nekunzwisisa pfungwa huru dzemasisitimu ekusaenzana kwemutsara.
