Exam #1 (Chp 1-4) - Business Analytics II

break even model components - total variable cost

Total variable cost (vcv)- function of volume (v) and unit variable cost.

which of the following could not be a linear programming problem constraint? a. 1A+2B ≠3 b. 1A+2B = 3 c. 1A+2B <= 3 d. 1A+2B >= 3

a

If fixed costs increase, but variable cost and price remain the same, the break even point ... a. decreases b. increases c. remains the same d. may increase or decrease depending on sales

b

optimal solution

the single best solution to a problem

steps in the management science process - Model Implementation (5)

•Model Implementation- Actual use of the model or its solution.

break even model components - volume

•Volume (v) - the number of units produced or sold

the management science process

1. Observation 2. Problem Definition 3. Model Construction 4. Solution 5. Implementation

18. at the break even point.... a. total revenue equals total cost b. profit is maximized c. revenue is maximized d. costs are maximized

a

if the price increases, but fixed and variable costs do not change, the break even point... a. decreases b. increases c. remains the same d. may increase or decrease, depending on sales

a

the result of an effective decision making process should be monitored in order to... a. reveal break even point b. reveal errors in the implementation c. keep fixed and variable costs distinct d. change the scientific method

b

________ involves determining the functional relationship between variables, parameter, and equations a. problem and observation b. problem definition c. model construction d. model solution

c

which variable is not a component of break even analysis? a. fixed costs b. variable costs c. number of employees d. number of customers

c

a model is a functional relationship that includes... a. variables b. parameter c. equations d. all the above

d

infeasible solution

violates at least one of the constraints Example: X1= 10 bowls X2= 20 mugs Z= 40X1+50X2=1400 Labor constraint check: 1(10)+2(20)= 50 > 40 hours

surplus variables

•A surplus variable is subtracted from a >= constraint to convert it to an equation (=) .•A surplus variable represents an excess above a constraint requirement level. •A surplus variable contributes nothing to the calculated value of the objective function. •Subtracting surplus variables in the farmer problem constraints: 2X1+4X2-S1=16 (Nitrogen) 4X1+3X2-S2=24 (phosphate)

22. if fixed costs decrease, but variable cost and price remain the same, the break even point... a. decreases b. increases c. remains the same d. may increase or decrease depending on sales

a

3. use the constraints given below and determine which of the following points is feasible 14x+6y <= 42 x-y<= 3 a. x= 1, y=4 b. x=2, y=8 c. x=2, y=4 d. x=3, y=0.5

a

____________ are generally independent of the volume of units produced and sold. a. fixed costs b. variable costs c. profits d. average cost

a

which of these disciplines typically does not fall under the umbrella of analytics... a. info systems b. statistics c. management science d. operations management

d

break even model components - variable costs

•Variable Cost (cv)- unit production cost of product.

feasible solution

A solution that satisfies all the constraints, and does not violate any of the constraints Example: X1= 5 bowls X2= 10 mugs Z= 40X1+50X2=700 labor constraint check: 1(5)+2(10)=25 <=40 hours Clay constraint check: 4(5)+3(10) = 70 <= 120 pounds

break-even analysis (profit analysis)

Break-Even Analysis (1 of 9) •Used to determine the number of units of a product to sell or produce that will equate total revenue with total cost .•The volume at which total revenue equals total cost is called the break-even point. •Profit at break-even point is zero.

example of model construction

Example of Model Construction (1 of 3) Information and Data: •Business firm makes and sells a steel product •Product costs $5 to produce •Product sells for $20 •Product requires 4 pounds of steel to make •Firm has 100 pounds of steel Business Problem: •Determine the number of units to produce to make the most profit, given the limited amount of steel available Example of Model Construction (2 of 3) Variables: x= # units to produce (decision variable) Z= total profit (in $) Model: Z= $20x − $5x (objective function) 4x= 100 lb of steel (resource constraint) Parameters:$20, $5, 4 lbs, 100 lbs (known values) Formal Specification of Model: maximize Z = $20x−$5x subject to 4x = 100

break even model components - fixed costs

Fixed Cost (cf)- costs that are independent of the number of units produced and remain constant.

Irregular Types of Linear Programming Problems

For some linear programming models, the general rules do not apply. Special types of problems include those with: •Multiple optimal solutions •Infeasible solutions •Unbounded solutions

Graphical Solution of LP Models

Graphical solution is limited to linear programming models containing only two decision variables(can be used with three variables but only with great difficulty). •Graphical methods provide a picture of how a solution for a linear programming problem is obtained.

Linear Programming (LP) Model Formulation

LP Model Formulation 1 (1 of 3) Resource Requirements product - Bowl, Mug Labor(Hr./Unit) Clay(Lb./Unit) Profit($/Unit) Bowl = 1 labor, 4 clay, 40 profit Mug = 2 labor , 3 clay , 50 profit Figure 2.1 Beaver Creek Pottery Company •Product mix problem - Beaver Creek Pottery Company •How many bowls and mugs should be produced to maximize profits given labor and materials constraints? •Product resource requirements and unit profit: LP Model Formulation 1 (2 of 3) Resource Availability: 40 hrs of labor per day 120 lbs of clay Decision Variables: x1 = number of bowls to produce per day x2 = number of mugs to produce per day Objective Function: Maximize Z = $40x1 + $50x2 Where Z = profit per day Resource Constraints: 1X1+2X2<=40hours of labor 4X1+3X2<=120 pounds of clay Non-Negativity Constraints X1>=0,X2>=0 LP Model Formulation 1 (3 of 3) Complete Linear Programming Model: Maximize: Z=$40X1+$50X2 Subject to: 1X1+2X2<=40 4X1+3X2<=120 X1,X2>=0

sensitivity analysis

Sensitivity analysis determines the effect on the optimal solution of changes in parameter values of the objective function and constraint equations. • Changes may be reactions to anticipated uncertainties in the parameters or to new or changed information concerning the model.

Objective Function Coefficient: Sensitivity Range

The sensitivity range for an objective function coefficient is the range of values over which the current optimal solution point will remain optimal. if the slope of the objective function changes to -4 /3 the line is parallel to the constraint line (next slide).

1. maximization problem, assume the constraint is binding. if the original amount of a resource is 4lbs. and the range of feasibility (sensitivity range) for this constraint is from 3lbs. to 6lbs., increasing the amount of this resource by 1lb. will result in... a. same product mix, different total profit b. different product mix, same total profit as before c. same product mix, same total profit d. different product mix, different total profit

a

11. which of the following statements about infeasible problems is the best? a. all of the possible solutions violate at least one constraint b. all of the possible solutions violate all of the constraints c. at least one of the possible solutions violates all of the constraints d. at least one of the possible solutions violates at least one of the constraints

a

5. in the formulation of a >= constraint... a. a surplus variable is subtracted b. a surplus variable is added c. a slack variable is subtracted d. a slack variable is added

a

6. which of the following statements is not true? a. an infeasible solution violates all constraints. b. a feasible solution point does not have to lie on the boundary of the feasible solution c. a feasible solution satisfies all constraints d. an optimal solution satisfies all constraints

a

variable cost: a. depends on the number of units produced. b. plus, marginal cost equals fixed cost c.is equal to total cost in deterministic models. d. is the same as average cost

a

which of these is an appropriate constraint for the problem? a. x1A+x1B+x1C = 320 b. x1A+x2A+x3A = 320 c. x3A+x3B+x3C = 460 d. x1A+x2B+x3B = 420

a

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.

13. a slack variable... a. is the amount by which the left side of a >= constraint is larger than the right side b. is the amount by which the side of a >= constraint is smaller than the right side. c. is the difference between the left and right side of a constraint d. exists for each variable in a linear programming problem.

b

3. which of the following could be a linear programming objective function? a. Z= 1A+2BC+3D b. Z= 1A+2B+3C+4D c. Z= 1A+2B/C+3D d. Z= 1A+2B^2+3D

b

7. without satisfying the non negativity constraint, a solution that satisfies all the other constraints of a linear programming problem is called... a. feasible b. infeasible c. semi feasible d. optimal

b

9. in order for an optimization problem to have multiple solutions... a. the objective function and one constraint must have the same y intercept b. the objective function and one constraint must have the same slope c. two or more of the constraints must not have intersect points d. two or more of the constraints must have the same slope

b

Decision variables... a. measure the objective function b. measure how much or how many items to produce, purchase, hire, etc c. always exist for each constraint d. measure the values of each constraint

b

The region that satisfies all of the constraints in a graphical linear programming problem is called the: a. region of optimality b. feasible solution space c. region of non negativity d. optimal solution space

b

if the price decreases, but fixed and variable costs do not change, the break even point... a. decreases b. increases c. remains the same d. may increase or decrease, depending on sales

b

variable cost does not include... a. raw materials and resources b. staff and management salaries c. material handling and freight d. direct labor and packaging

b

4. sensitivity analysis is the analysis of the effect of _______ changes on the _________ ... a. price, company b. cost, production c. parameter, optimal solution d. constraint, parameter

c

Balanced Transportation Problems have which of the following type of constraint? a. >= b. <= c. = d. <

c

When systematically formulating a linear program, the first step is to: a. construct the objective function b. formulate the constraints c. identify the decision variables d. identify the parameter values

c

___________ is used to analyze changes in model parameters... a. optimal solution b. feasible solution c. sensitivity analysis d. a slack variable

c

the components of break even analysis are... a. cost and profit b. volume and cost c. volume, cost, and profit d. Volume and profit

c

the field of management science... a. approaches decision making irrationally with technique based on the scientific method b. is another name for management or human resources management c. concentrates on the use of quantitative methods to assist managers in decision making. d.is completely separate and distinct from all other disciplines

c

the indicator that results in total revenues being equal to total cost is called... a. marginal coast b. marginal volume c. break even point d. profit mix

c

the processes of problem observation: a. cannot be done until alternatives are proposed b. requires consideration of multiple criteria c. is the first step of decision making d. is the final step of problem solving

c

the term __________ refers to testing how a problem solution reacts to changes in one or more of the model parameters a. graphical solution b. decision analysis c. sensitivity analysis d. break even point

c

there is a considerable overlap in the scientific method and management science techniques. which of the following steps is shared between them? a. observation b. problem definition c. model construction d. implementation

c

which of the following is an equation or an inequality that expresses a resource restriction in a mathematical model? a. a decision variable b. an objective function c. a constraint d. a parameter

c

which steps of the management science process can be either recommended decision or information that helps a manger make a decision? a. model implementation b. problem definition c. model solution d. problem formulation

c

decision variables

controllable inputs; decision alternatives specified by the decision maker, such as the number of units of a product to produce

12. Multiple optimal solutions can occur when the objective function is ________ a constraint line. a. unequal to b. equal to c. perpendicular to d. parallel to

d

2. a plant manager is attempting to determine the production schedule of various products to maximize product. assume that a machine hour constraint is binding. if the original amount of machine hours available is 200 minutes, and the range of the feasibility is from 130 minutes to 300 minutes, providing two additional machine hours will result in... a. same product mix, different total profit b. different product mix, same total profit as before c. same product mix, same total profit d. different product mix, different total profit It should be noted that in a situation whereby constraint is binding and a change with regards to the availability that is within the range exist, this will bring about a change in both the product mix and total profit.

d

an optimization problem that has multiple optimal solutions ... a. means that there are actually no optimal solutions b. is reflected by the entire feasible region being optimal c. means that the surplus for a third constraint cannot be calculated d. provides the decision maker with increased flexibility

d

the purpose of break even analysis is to determine the number of units of a product to sell that will... a. appeal to the consumer b. result in profit c. result in loss d. result in zero profit

d

decision variables

mathematical symbols representing levels of activity by the firm.

parameters

numerical coefficients and constants used in the objective function and constraints.

constraints

requirements or restrictions placed on the firm by the operating environment, stated in linear relationships of the decision variables.

optimal solution point

the last point the objective function touches as it leaves the feasible solution area

management science and business analytics

•Business analytics uses large amounts of data with management science techniques to help managers make decisions •Brings together information technology, statistics, management science, computer science, engineering, and data science •Big data

analytical career skills

•Critical thinking - purposeful and goal-oriented problem definition and solution •Collaborating - necessary in a project team-based environment •Information Technology & Computing - reliance on computer software •Data Literacy - ability to access, interpret, manipulate, communicate and summarize data

the management science approach

•Management science is a scientific approach to solving management problems. •It is used in a variety of organizations to solve many different types of problems. •It encompasses a logical mathematical approach to problem solving. •Management science, also known as operations research, quantitative methods, business analytics, etc., involves a philosophy of problem solving in a logical manner.

steps in the management science process - Model Construction (3)

•Model Construction- Development of the functional mathematical relationships that describe the decision variables, objective function and constraints of the problem.

steps in the management science process - Model Solution (4)

•Model Solution- The model is solved using management science techniques.

steps in the management science process - observation (1)

•Observation- Identification of a problem that exists (or may occur soon) in a system or organization.

steps in the management science process - Problem Definition (2)

•Problem Definition- The problem must be clearly and consistently defined, showing its boundaries and interactions with the objectives of the organization.

slack variables

•Standard form requires that all constraints be in the form of equations (equalities). •A slack variable is added to a constraint(weak inequality) to convert it to an equation (=) .•A slack variable typically represents an unused resource. •A slack variable contributes nothing to the objective function value.

break-even analysis

•Total Cost (TC) - total fixed cost plus total variable cost. •Profit (Z) - difference between total revenue vp(p = unit price) and total cost, i.e.