# CHEAT ```=IF(this happens, this, if not)
Break even = \$G\$26
When building optimization LP:
Decision variable:
x = number of…
y = number of…
Formulation:
(objective)
Min/Max
#x+#y
(constraints)
Subject to
#x+#y &gt;= #
x, y &gt;= 0
x, y = {0,1}
Optimal solution x=# y=# **(x,y)**
.
Como graficar: 4x+10y=100
Si x=0 obtienes y
Feasible region
when min
Slack (for ≤ type constraints): amount of a
constraint that is unused by a solution
Surplus (for ≥ type constraints): amount by which
a constraint is exceeded by a solution
Redundant = not affecting constraint
Unbounded problem: objective function value is œ
OptSol= (FV*ObjCoe)+(2FV*2ObjCoe)
1E+ = infinite
BINDING CONTRAINT: FV=RHS
NON BC= SP 꼭 0
Effect on OptSol = Change*SP
Uniform change in coefficients don’t affect OptSol
Prior probability: P(A1) through P(An)
outcome before considering
the new evidence
o Likelihood: P(B|A1) through P(B|An)
The probability we would see the evidence
given that the event happens
o Posterior probability: P(A1|B) through
P(An|B)
evidence
P(A|B) =
P(B|A) P(A)
P(B|A) P(A )+P(B|notA)P(notA)
Define 𝑌𝑖= {1 𝑖𝑓 .. in𝑖, 0 𝑜𝑡ℎ𝑒𝑟𝑤𝑖𝑠𝑒. for i = {1,2,3,4,5}
Minimize 2 Y1 + 1.5 Y2 +3 Y3 + Y4 +3 Y5 (===Cost x1)
Y2 + Y3 ≥ 1 (City 3 has to be covered)
NON LINEAR (xy, x^2)
max Σ 𝑋s,c ∗ 𝑃𝑅𝐸𝐹s,c
subject to Σ 𝑋c,c ≤ 1 for all c
Σ 𝑋s,c ≤ 1 for all s
Σ 𝑋s,c ∗ 𝑃𝑅𝐸𝐹s,c ≥ 1 for all s
𝑋s,c binary for all s and c
Certainty Equivalent (CE): guaranteed return that someone would accept now, rather than taking
a chance on a higher, but uncertain, return in the future
o Risk premium (RP) = Expected value - Certainty equivalent
o Different individuals have different CEs and RPs for the same circumstance. That is, they have
different attitudes toward risk.
□ Risk averse: CE &lt; EV, RP &gt; 0
□ Risk neutral: CE = EV, RP=0
□ Risk seeking: CE &gt; EV, RP &lt; 0
o Step 1: Develop a payoff table using monetary values
o Step 2: Identify the best and worst payoff values in the table and assign each a utility, with U(best
payoff) &gt; U(worst payoff). **BEST PAYOFF U(20,000) = 10 (mayor a worst)
utility:
between a guaranteed payoff of
and a gamble in which there is a
worst payoff
b) Calculate the utility of
payoff)
o Step 4: Apply the expected utility approach to the utility table and select the decision alternative
with the highest expected utility
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