AGEC 3414 EXAM 1 BISWAS
Total Cost (TC)
total fixed cost plus total variable cost.
variable costs
unit production cost of product.
price (p)
unit revenue from product sales.
linear programming
uses linear algebraic relationships to represent a firm's decisions, given a business objective, and resource constraints.
constraint
what represents an inequality or equation that expresses a restriction in a mathematical model of a business management decision problem?
total revenue equal total profit
which of the following is true at the break-even point to cover fixed costs? a. total fixed costs equals total profit b. total revenue equal total profit c. total variables cost equals total fixed cost d. at the production quantity, proft equals zero
Characteristics of Linear Programming Problems
- A decision among alternative courses of action is required - The decision is represented in the model by decision variables. - The problem encompasses a goal, expressed as an objective function, that the decision-maker wants to achieve. - Restrictions (represented by constraints) exist that limit the extent of achievement of the objective. - The objective and constraints must be definable by linear mathematical functional relationships.
$160 Given: Number of rooms booked in a month to break even = 300 Fixed cost per month = $6,000 Revenue from 1 booked room = $180 Then, Revenue from 300 booked rooms = 180*300 = $54,000 Let the variable cost for 1 occupied room = x Then, Variable cost 300 occupied rooms = 300x Now, Total cost per month = (Fixed cost per month)+(Variable cost 300 occupied rooms) = 6000+300x For the break even, Total cost per month = Revenue from 300 booked rooms 6000+300x = 54000 300x = 54000-6000 300x = 48000 x = 48000/300 x = $160
A bed-and-breakfast breaks even every month if they book 300 rooms over the course of a month. Their fixed cost is $6000 per month and the revenue they receive from each booked room is $180. What is their variable cost per occupied room.
setting up a spreadsheet with complex models and formulas.
A difficult aspect of using spreadsheets to solve management science problems is
all the above
A linear programming model consists of A) decision variables B) an objective function C) constraints D)all the above
interfaces
Applications journal published by Institute for Operations Research and Management Sciences (INFORMS)
linear mathematical programming
Clear objective; Restrictions on resources and requirements; Parameters known with certainty
decision variables objective function constraints sensitivity analysis
Components of Break-even Analysis
divisibility
Decision variables can take on any fractional value and are therefore continuous as opposed to integer in nature
measure how much or how many items to produce, purchase, hire, etc.
Decision variables measure what
model construction
Development of the functional mathematical relationships that describe the decision variables, objective function and constraints of the problem.
$18 Given: Cost of producing 1 unit = $3 Fixed monthly cost of operating the production facility = $3000 Monthly demand for part #2206 = 200 units Let the selling price of 1 unit of part #2206 = x Then, Revenue from selling 200 units = 200*(Selling price of 1 unit) = 200x Also, the total cost of producing 200 units is given as, Total cost of producing 200 units = (Cost of producing 200 units)+(Fixed monthly cost of operating the production facility) = 200*3+3000 = 600+3000 = $3,600 For the break-even, Revenue from selling 200 units = Total cost of producing 200 units 200x = 3600 x = 3600/200 x = $18 Thus, the correct option for the amount to be charged for each part is C) $18.
EKA manufacturing company produces part #2206 for the aerospace industry. The unit production cost of part #2206 is $3. The fixed monthly cost of operating the production facility is $3000. Next month's demand for part #2206 is 200 units. How much should the company charge for each unit of part #2206 to break even?
Multiple optimal solutions Infeasible solutions Unbounded solutions
For some linear programming models, the general rules do not apply. the special types of problems include those with:
Visualization
Graphical methods provide ___________ of how a solution for a linear programming problem is obtained.
Conditions that impact the parameters of a model , such as unit profit, may change over time and render them inaccurate.
How is it possible for the parameters of a model to be accurate initially and then become inaccurate at a later date?
observation
Identification of a problem that exists (or may occur soon) in a system or organization
Decrease supply in the current year
In a commodity supply and use table, a decrease in a production value estimate would have what affect?
parameters
In real applications of linear programming, many of the _______ in the model may be only rough estimates.
No, if the optimal solution will remain the same over a wide range of values for a coefficient, then it may be appropriate to make only a fairly rough estimate for the parameter of a model.
Is it always inappropriate to make only a fairly rough estimate for a parameter of a model? Why?
2500 units Fixed cost of production = $50,000 Variable cost = $25 Revenue per unit = $45 Let the number of units produced be x. Then, cost function is given by: C(x) = 50000+25x Revenue function is: R(x) = 45x At break even point: C(x) = R(x) 50000+25x = 45x 50000 = 45x-25x 50000 = 20x 50000/20 = x 2500 = x
It costs $50,000 to start a production process. Variable cost is $25 per unit and revenue in $45 per unit. What is the break-even point?
known with certainty
Linear mathematical programming techniques assume that all parameter in the models are ______________.
operations research, quantitative methods, business analytics, etc.
Management science is also known as
network techniques
Model often formulated as diagram; Deterministic or probabilistic
model solution
Models solved using management science techniques
maximizing profit or minimizing costs
Objectives of business decisions frequently involve _________ or _________.
- proportionality -additivity -divisibility -certainty
Properties of Linear Programming Models
Performance measures
Quantitative expressions of goals or objectives in business analysis problems are called what?
Probabilistic techniques
Results contain uncertainty
observation problem defintion model construction model solution model implementation
Steps in the management of science process
TRUE
T/F A management science solution can be either a recommended decision or information that helps a manager make a decision
TRUE
T/F A model is a mathematical representation of a problem situation including variables, parameters, and equations.
true
T/F Constraints usually appear as equations that are less than, equal to, or greater than a parameter.
false
T/F Data and equations required to solve a business problem can be entered into a specific computer software program before the mathematical model of the problem is developed.
True In graphical solutions, any problem having multiple optimal solutions will have an infinite number of them, each with the same optimal value of the objective function.
T/F Graphical solutions to linear programming problems have an infinite number of poosible objective function lines.
FALSE
T/F If variable costs increase, but price and fixed costs are held constant, the break-even point will decrease.
false The objective function can be maximized if the company is aiming at maximizing their profit or sales, the objective function can also be minimized for instance if the aim is to find the minimum expense. Therefore depending on the objective of the company, the function can be maximized or minimized.
T/F In linear programming models, objective functions can only be maximized.
False
T/F Linear programming model can have either < or > inequality constraints but not both in the same problem.
False
T/F Linear programming models can only solve decision problems that maximize revenue or profit.
false management science is a branch that focus on managerial decision to solve problems through scientific approach. Whereas, management science modelling technique focuses on construction of models to solve problems.
T/F Management science techniques focus primarily on observation, model construction, and implementation to find an appropriate solution to a problem.
true
T/F Sensitivity analysis can be used with almost any management science procedure, not just linear programming.
false - Slack variables are associated with maximization as well as minimization problem. It is used to transform an inequality constraint to equality.
T/F Slack variables are only associated with maximization problems
true
T/F The feasible solution area contains infinite solutions to the linear program.
True
T/F The objective function P=3x1+5x2+4x3 is linear.
false
T/F The proportionality assumption of linear programming implies that decisions variables are allowed to have noninteger values in the optimal solution.
False. The break-even point will increase when the number of fixed costs and expenses increases. The Break-even point also increases when the variable expenses increase without a corresponding increase in the selling price.
T/F in general, an increase in price increases the break-even point if all costs are held constant.
true
T/F management science analysis is said to only "aid" business decisions of qualitative factors.
true
T/F operations research is another name commonly used for the field of management science.
true
T/F the simplex method os the name of the mathematical algorithm.
false In linear programming problem the objective function and constraint both are linear function(degree 1) of decision variable. In case of multiplicative the function will not remain linear hence the given statement is false.
T/F the terms in the objective function or constraints are multiplicative.
additivity
Terms in the objective function and constraint equations must be additive
the range of values for a specific objective function coefficient over which the optimal solution point, xi (i= 1 and 2 in the pottery example) will remain optimal.
The focus of Sensitivity analysis is to determine _________________________________________________________.
two
The graphical solution is limited to linear programming models containing only _____ decision variables (can be used with three variables but only with great difficulty).
problem definition
The problem must be clearly and consistently defined, showing its boundaries and interactions with the objectives of the organization.
range of values over which the current optimal solution point will remain optimal.
The sensitivity range for an objective function coefficient is the what?
the allowable range for each coefficient in the objective function.
The sensitivity report generated by the Excel Solver reveals what?
Sensitivity Analysis
The term _____ refers to testing how a problem solution reacts to changes in one or more of the model parameters.
break-even point
The volume at which total revenue equals total cost is called the ________. TR=TC
TC=Cf+VCv -> fixed costs + total variable costs
Total Cost (TC) formula
Break-even analysis
Used to determine the number of units of a product to sell or produce that will equate total revenue with total cost.
certainty
Values of all the model parameters are assumed to be known with certainty (non-probabilistic).
other techniques
Variety of deterministic and probabilistic methods for specific types of problems including forecasting, inventory, simulation, multicriteria, etc.
Sensitivity analysis reveals which parameter estimates are sensitive. A parameter is considered sensitive if even a small change in its value can change the optimal solution.
What does sensitivity analysis reveal about the parameters of a model that are only estimates?
surplus variable
______ contributes nothing to the calculated value of the objective function.
Proportionality
_______ is the rate of change (slope) of the objective function and constraint equations is constant.
standard form
_______ requires that all constraints be in the form of equations (equalities).
Management science scientific method
_________ encompasses a logical, systematic approach to problem solving, which closely parallels the _________.
sensitivity analysis
__________ determines the effect on the optimal solution of changes in parameter values of the objective function and constraint equations. It is studying how changes in the parameters of a linear programming model affect the optimal solution.
slack variable
__________ is added to a < constraint (weak inequality) to convert it to an equation.
graphical methods
___________ provide visualization of how a solution for a linear programming problem is obtained.
sensitive parameters
____________ are those parameters where a relatively small change in their values can change the optimal solution.
Graphical solution
_____________ is limited to linear programming models containing only two decision variables (can be used with three variables but only with great difficulty).
allowable range for an objective function coefficient
_______________ is the range of values for a particular coefficient in the objective function over which the optimal solution for the original model remains optimal.
surplus variable
a _______ represents an excess above a constraint requirement level.
feasible solution
a _________ does not violate any constraints
surplus variable
a _________ is subtracted from a > constraint to convert it to an equation.
slack variable
a _________ typically represents an unused resource and contributes nothing to the objective function value.
objective function
a linear mathematical relationship describing an objective of the firm, in terms of decision variables - this function is to be maximized or minimized.
functional relationship
a model which includes variables, parameters and equations.
model implementation
actual use of the model or its solution
infeasible solution
an ________ violates at least one of the constraints
model
an abstract mathematical representation of a problem situation including variables, parameters, and equations.
sensitivity analysis
an analysis of how the recommendations of a model might change if any of the parameter estimates in the model needed to be altered or corrected
Decision variables
are algebraic variables that represents a quantifiable decision to be made.
constraints
are inequalities or equations that express some restrictions on the values that can be assigned to decision variables.
parameters
are known, constant values that are usually coefficients of variable in equations
Variables
are symbols used to represent an item that can take on any value. They are unknown.
- Project Planning - Capital Budgeting - Inventory Analysis - Production Planning - Scheduling
business usage of management science; some applications areas:
model variables parameters data functional relationships
components of model construction
fixed costs
costs that remain constant regardless of number of units produced
profit (Z)
difference between total revenue vp (p = unit price) and total cost, i.e. Z=vp-(Cf+VCv)
Total Revenue (TR)
function of a unit price and volume.
total variable cost
function of volume (v) and unit variable cost.
$614
if a $525 cost in year 1 is expected to increase 4% per year, what is its value in year 5?
decreases
if fixed costs decrease, but variable cost and price remain the same, the break-even point ________
violates
in relations to an infeasible problem: every possible solution _____ at least one constraint
increases
in relations to an unbounded problem: value of the objective function _______ indefinitely
parallel
in relations to multiple optimal solutions: the objective function is _______ to a constraint line
objective function
is a mathematical expression that gives the measure of performance for the problem in terms of the decision variables.
linear algebraic relationships
linear programing uses ______________ to represent a firm's decisions, given a business objective, and resource constraints.
1. identify problem as solvable by linear programming. 2. Formulate a mathematical model of the unstructured problem. 3. solve the model. 4. implementation
linear programing: steps in application
decision variables
mathematical symbols representing levels of activity by the firm
parameters
numerical coefficients and constants used in the objective function and constraints.
data
pieces of information from the problem environment.
zero
profit at break-even point is _____.
constraints
requirements or restrictions placed on the firm by the operating environment, stated in linear relationships of the decision variables.
standard form
requires all variables in the constraint equations to appear on the left of the inequality (or equality) and all numeric values to be on the right-hand side.
Step 1 : Define the decision variables Step 2 : Define the objective function Step 3 : Define the constraints
summary of linear programming Model Formulation Steps
volume (v)
the number of units produced or sold
