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Quant Midterm: Optimization

question
Optimization
answer
finding the best possible answer to the problem at hand
question
3 questions of Optimization and describe what they are trying to find
answer
1. Goal/Objective: What are we trying to accomplish?
2. Decision Variables: What is/are the decisions?
3. Constraints: What rules do we have to obey along the way?
question
Optimization Steps
answer
1. Formulate problem: decision variables, obj. function ($P x A) + ($P x B), constraints
2. Check whether we can satisfy the demand: if so compute profit
3. If Demand can't be satisfied: identify the bottleneck, compute bang for buck, and identify preferred product
4. Compute the values of Decision Variables: how many units to make of each product
-conduct sensitivity analysis
question
Optimal Production Quantities
answer
How much of each product we can make that maximizes profit
question
Objective Function Value (OFV)
answer
value of the objective function when your produce optimal produce quantities (multiply profits to their respective optimal unit output and sum)
question
Sensitivity Analysis
answer
due to market conditions, profit per unit and resource availability may change
question
If there is a decrease in objective function coefficient what will happen?
answer
the meaning and use of "allowable" decreases
-Objective function Coefficient (OFC): the profit changes
question
Range of no change
answer
changes in profit value that does not change our preferred profit
question
allowable decrease
answer
decrease in coefficient (profit) allowed before change in preferred product
-for other products, it is the profit price: cannot go under $0
question
Allowable increase
answer
increase in coefficient (profit) allowed before you change your preferred product (for preferred product, it is infinity)
question
Shadow Price (SP)
answer
change in the objective function value for a unit change in right hand side (RHS) of the constraint (resource availability demand)

-change in OFC for a unit change in RHS
-change in OFC/ Change in RHS
question
Slack
answer
RHS-LHS: leftover resources
-demand SP is in terms of $/unit for demand or change in net profit/ change in # of units
question
If demand is not met
answer
-there is slack
-SP = $0
question
If slack >0 the shadow price is --
answer
$0
question
SP tells us
answer
-reservation price
-marginal cost
-max price we should pay
-constraints
question
Reservation price
answer
how much we should pay for overtime of bottleneck worker
question
Marginal Cost
answer
cost of producing one additional unit of the resource

-SP is the marginal cost of resources/constraints
question
Max price we should pay
answer
SP+ Current Price
question
What if demand increases, how does OFV Change?
answer
-multiply increase by profit
-decrease by what you lost from ongoing production of the other variable for net increase
-stealing
-shadow price for demand constraint
question
Stealing
answer
reallocating the time from one unit to increase production of the preferred product
question
Shadow price for demand constraint
answer
net increase/change in demand
question
Bottleneck
answer
-decides our profit, output, and product
-resource which limits/constrains other resources to produce their full potention
question
True/False: If Slack = 0, it is the bottleneck
answer
false
question
utilization
answer
-time used in producing # of units/ total time available or # of units produced/ resource capacity
-when utilization =1--%, full capacity
question
Free/Idle Time
answer
total time available- time used to produce # of units
question
Why merge?
answer
-to maximize rev and market dominance
-economies of scale: combine productions to lower marginal costs
-synergies: combine resources
question
Preferred product
answer
=profit/time per unit (whichever is greater for bottleneck resource)
question
Market instinct
answer
to meet the demand of the product with more profit per unit (wrong)
question
"bang for buck"
answer
when analyzing the bottleneck for each product, choose the one whose profit per minute is greater (preferred product)
-profit/time per unit of bottleneck
question
Marginal Cost
answer
(shadow price)
-should not pay resources more than marginal cost
-reduced cost= MR-MC (marginal rev-marginal cost)
-MR=MC (do not produce if MC>MR
1 of 30
question
Optimization
answer
finding the best possible answer to the problem at hand
question
3 questions of Optimization and describe what they are trying to find
answer
1. Goal/Objective: What are we trying to accomplish?
2. Decision Variables: What is/are the decisions?
3. Constraints: What rules do we have to obey along the way?
question
Optimization Steps
answer
1. Formulate problem: decision variables, obj. function ($P x A) + ($P x B), constraints
2. Check whether we can satisfy the demand: if so compute profit
3. If Demand can't be satisfied: identify the bottleneck, compute bang for buck, and identify preferred product
4. Compute the values of Decision Variables: how many units to make of each product
-conduct sensitivity analysis
question
Optimal Production Quantities
answer
How much of each product we can make that maximizes profit
question
Objective Function Value (OFV)
answer
value of the objective function when your produce optimal produce quantities (multiply profits to their respective optimal unit output and sum)
question
Sensitivity Analysis
answer
due to market conditions, profit per unit and resource availability may change
question
If there is a decrease in objective function coefficient what will happen?
answer
the meaning and use of "allowable" decreases
-Objective function Coefficient (OFC): the profit changes
question
Range of no change
answer
changes in profit value that does not change our preferred profit
question
allowable decrease
answer
decrease in coefficient (profit) allowed before change in preferred product
-for other products, it is the profit price: cannot go under $0
question
Allowable increase
answer
increase in coefficient (profit) allowed before you change your preferred product (for preferred product, it is infinity)
question
Shadow Price (SP)
answer
change in the objective function value for a unit change in right hand side (RHS) of the constraint (resource availability demand)

-change in OFC for a unit change in RHS
-change in OFC/ Change in RHS
question
Slack
answer
RHS-LHS: leftover resources
-demand SP is in terms of $/unit for demand or change in net profit/ change in # of units
question
If demand is not met
answer
-there is slack
-SP = $0
question
If slack >0 the shadow price is --
answer
$0
question
SP tells us
answer
-reservation price
-marginal cost
-max price we should pay
-constraints
question
Reservation price
answer
how much we should pay for overtime of bottleneck worker
question
Marginal Cost
answer
cost of producing one additional unit of the resource

-SP is the marginal cost of resources/constraints
question
Max price we should pay
answer
SP+ Current Price
question
What if demand increases, how does OFV Change?
answer
-multiply increase by profit
-decrease by what you lost from ongoing production of the other variable for net increase
-stealing
-shadow price for demand constraint
question
Stealing
answer
reallocating the time from one unit to increase production of the preferred product
question
Shadow price for demand constraint
answer
net increase/change in demand
question
Bottleneck
answer
-decides our profit, output, and product
-resource which limits/constrains other resources to produce their full potention
question
True/False: If Slack = 0, it is the bottleneck
answer
false
question
utilization
answer
-time used in producing # of units/ total time available or # of units produced/ resource capacity
-when utilization =1--%, full capacity
question
Free/Idle Time
answer
total time available- time used to produce # of units
question
Why merge?
answer
-to maximize rev and market dominance
-economies of scale: combine productions to lower marginal costs
-synergies: combine resources
question
Preferred product
answer
=profit/time per unit (whichever is greater for bottleneck resource)
question
Market instinct
answer
to meet the demand of the product with more profit per unit (wrong)
question
"bang for buck"
answer
when analyzing the bottleneck for each product, choose the one whose profit per minute is greater (preferred product)
-profit/time per unit of bottleneck
question
Marginal Cost
answer
(shadow price)
-should not pay resources more than marginal cost
-reduced cost= MR-MC (marginal rev-marginal cost)
-MR=MC (do not produce if MC>MR
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