MAS 801 It's a Discreetly Discrete World – Mathematics in Real-life ...
MAS 801 It's a Discreetly Discrete World – Mathematics in Real-life ...
MAS 801 It's a Discreetly Discrete World – Mathematics in Real-life ...
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Lecture 9: 22 October 2008<br />
Prov<strong>in</strong>g Optimality: Method of Tight Restrictions<br />
• Let’s multiply the 1st constra<strong>in</strong>t throughout by a nonnegative number a<br />
ax + 2ay ≤ 300a<br />
• Let’s multiply the 2nd constra<strong>in</strong>t throughout by a nonnegative number b<br />
• Add<strong>in</strong>g these two constra<strong>in</strong>ts give<br />
maximize z = 1000x + 3000y<br />
subject to x + 2y ≤ 300<br />
x + 5y ≤ 600<br />
x ≥ 0<br />
y ≥ 0<br />
bx + 5by ≤ 600b<br />
(a+b)x + (2a+5b)y ≤ 300a + 600b<br />
• If we want the left hand side to be 1000x + 3000y we need<br />
a + b = 1000 and 2a + 5b = 3000
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