COB 291 review

What would be the value added by a market analysis undertaken if the expected value with sample information is $8.56 million and the expected value without sample information is $6.39 million?

$2.17 million

The equation of the line representing the constraint 4x1 + 2x2 ≤ 100 passes through the points:

(25,0) and (0,50)

exhibit 1The following questions are based on the output below.A store currently operates its service system with 1 operator. Arrivals follow a Poisson distribution and service times are exponentially distributed. The following spreadsheet has been developed for the system. M/M/s queuing computations Arrival rate 6 Service rate 8 Number of servers 1 (max of 40) Utilization 75.00% P(0), probability that the system is empty 0.2500 Lq, expected queue length 2.2500 L, expected number in system 3.0000 Wq, expected time in queue 0.3750 W, expected total time in system 0.5000 Probability that a customer waits 0.7500 What is the probability that a customer must wait in queue before being served?

.75

Given this frequency distribution, the random number 0.4258 would be interpreted as a demand of: Demand. Probability 0. 0.38 1. 0.22 2 0.22 1 0.18

1

If the arrival process is modeled as a Poisson random variable with arrival rate λ, then the average time between arrivals is

1/λ

A typical transportation problem has 4 sources and 3 destinations. How many decision variables would there be in the linear program for this?

12

A company has recorded the following list of service rates (customers/hour) for one of its servers. What is the mean service time for this server? ​ Customers / hour: 4, 4, 5, 6, 5, 4, 3, 4, 3, 5, 5, 6

13.3 min

If the forecasted value of the time series variable for period 2 is 22.5 and the actual value observed for period 2 is 25, what is the forecast error in period 2?

2.5

A diet is being developed which must contain at least 100 mg of vitamin C. Two fruits are used in this diet. Bananas contain 30 mg of vitamin C and Apples contain 20 mg of vitamin C. The diet must contain at least 100 mg of vitamin C. Which of the following constraints reflects the relationship between Bananas, Apples and vitamin C?

20 A + 30 B ≥ 100

Suppose that the payoffs for an alternative with three states of nature are: 10, 20, and 30. The probabilities of these states of nature are 0.2, 0.3, and 0.5, respectively. The expected payoff for the alternative is equal to

23

The constraint for resource 1 is 5 X1 + 4 X2 ≤ 200. If X1 = 20, what it the maximum value for X2?

25

Suppose for a particular week, the forecasted sales were $4,000. The actual sales were $3,000. What is the value of the mean absolute percentage error?

33.3%

The production planner for Fine Coffees, Inc. produces two coffee blends: American (A) and British (B). He can only get 300 pounds of Colombian beans per week and 200 pounds of Dominican beans per week. Each pound of American blend coffee requires 12 ounces of Colombian beans and 4 ounces of Dominican beans, while a pound of British blend coffee uses 8 ounces of each type of bean. Profits for the American blend are $2.00 per pound, and profits for the British blend are $1.00 per pound. The goal of Fine Coffees, Inc. is to maximize profits. What is the constraint for Dominican beans?

4A + 8B ≤ 3,200.

Which objective function has the same slope as this one: 4x + 2y = 20.

4x + 2y = 10

The constraint for resource 1 is 5 X1 + 4 X2 ≤ 200. If X1 = 20 and X2 = 5, how much of resource 1 is unused?

80

Consider the table below. Suppose that you want to minimize the total distance traveled between groves and plants. How many decision variables must be used to model this?

9

The Sensitivity Report includes:

All of these. Analysis of the changes in the objective function coefficients. Analysis of the changes in the RHS values. Analysis of the changes in the constraint coefficients.

Which one of the following statements is not correct when making decisions?

All probabilities are assumed to be equal.

The Sensitivity Report includes:

Analysis of the changes in the objective function coefficients. Analysis of the changes in the RHS values. Analysis of the changes in the constraint coefficients. All of these

_____ are graphical representations of the decision problems that show the sequential nature of the decision-making process.

Decision trees

The first step in formulating ILP problems is:

Defining the decision variables.

The reduced cost for a variable is

Equal to the per unit amount the product contributes to profits minus the per unit value of the resources it consumes.

If a constraint has the equation 5x1 + 2x2 ≤ 60, then the constraint line passes through the points (0,12) and (30,0).

False

Payoffs always represent profits in decision analysis problems.

False

States of nature are alternatives available to a decision maker.

False

What is the goal in optimization?

Find the decision variable values that result in the best objective function and satisfy all constraints.

Resources in excess supply

Have a shadow price of zero.

Suppose that you solved a LP relaxed formulation of the maximization problem and found that the optimal objective function value is 500. The objective function value for the optimal solution to the original ILP problem can never be:

Higher than 500, which is the objective function value for the optimal solution to its LP relaxation.

Sanderson Manufacturing produces ornate, decorative wood frame doors and windows. Each item produced goes through three manufacturing processes: cutting, sanding, and finishing. Each door produced requires 1 hour in cutting, 30 minutes in sanding, and 30 minutes in finishing. Each window requires 30 minutes in cutting, 45 minutes in sanding, and 1 hour in finishing. In the coming week Sanderson has 40 hours of cutting capacity available, 40 hours of sanding capacity, and 60 hours of finishing capacity. Assume all doors produced can be sold for a profit of $500 and all windows can be sold for a profit of $400. Select the correct LP model for this problem. Let D represent Number of doors produced.Let W represent Number of windows produced. IMIN500D + 400WST1D + 0.5W ≤ 400.5 D + 1W ≤ 400.5 D + 0.75W ≤ 60D, W ≥ 0 IIMAX500D + 400WST1D + 0.5W ≤ 400.5 D + 0.75W ≤ 600.5 D + 1W ≤ 40D, W ≥ 0 IIIMAX500D + 400WST1D + 0.5W ≤ 400.5 D + 0.75W ≤ 400.5 D + 1W ≤ 60D, W ≥ 0 IVMIN500D + 400WST1D + 0.5W ≥ 600.5 D + 0.75W ≥ 400.5 D + 1W ≥ 40D, W ≥ 0

III

If the allowable increase for a constraint is 10 and we add 11 units of the resource what happens to the objective function value?

Increase by unknown amount.

The standardized queuing system notation such as M/M/1 or M/G/2 is referred to as

Kendall notation.

A doctor's office only has 8 chairs. The doctor's service times and customer inter-arrival times are exponentially distributed. What type of system is it?

M/M/1 with Finite Queue

Mocha Marketing Services owns 15 identical printers that print brochures and signages for various businesses. Printers breakdowns follow a Poisson distribution with an average of 0.03 breakdowns per operating hour per printer. The company employs one technician to fix these printers. Service times to repair the printers are exponentially distributed with an average of one hour per repair. What queueing model this system represent?

M/M/s model with finite arrival population

Which of the following measures of forecast accuracy is susceptible to the problem of positive and negative forecast errors offsetting one another?

Mean forecast error

A canned food manufacturer has its manufacturing plants in three locations across a state. Their product has to be transported to 3 central distribution centers, which in turn disperse the goods to 72 stores across the state. Which of the following is most likely to be the objective function in this scenario?

Minimizing the cost of shipping goods from the plant to the store

Transportation problem is an example of a category of problems that can be modeled as __________ problems.

Network flow

The first step in implementing LP problems in a spreadsheet is:

Organize the data for the model on the spreadsheet.

The proper sequence of steps in implementing the model in Excel presented in the textbook is:

Organize the data, represent the decision variables, represent the objective function, represent the constraints, and represent the bounds on the decision variables.

The allowable increase for a constraint is

The allowable increase for a constraint is the amount by which the resource can increase given shadow price.

Which of the following is a reason to employ queuing theory?

To reduce customer wait time in line.

When do alternate optimal solutions occur in LP models?

When a binding constraint is parallel to a level curve.

There are four possible projects. Write the constraint requiring that at most one of project 1 and 2 most be selected. Variables Xi = 1 if Projet i is selected, 0 otherwise.

X1 + X2 ≤ 1

When a manager considers the effect of changes in an LP model's coefficients he/she is performing

a sensitivity analysis.

For a Poisson random variable, λ represents the ____ number of arrivals per time period

average

The expected value of perfect information (EVPI) is used to

determine whether or not to invest resources to obtain better information.

A production optimization problem has 4 decision variables and a requirement that at least b1 units of material 1 are consumed. Which of the following constraints reflects this fact?

f(X1, X2, X3, X4) ≥ b1

A decision tree never start with a chance node. It always start with a decision node.

false

In linear programming, solutions that satisfy all of the constraints simultaneously are referred to as:

feasible.

Benefits of sensitivity analysis include all the following except:

fosters managerial acceptance of the optimal solution.

Given an objective function value of 150 and a shadow price for resource 1 of 5, if 10 more units of resource 1 are added (assuming the allowable increase is greater than 10), what is the impact on the objective function value?

increase of 50

Forecast error _____.

is associated with measuring forecast accuracy

If the shadow price for a resource is 0 and 150 units of the resource are added what happens to the optimal solution?

no change

A distribution of a random variable for which values extremely larger or smaller than the mean are increasingly unlikely can possibly be modeled as a(n) _____ probability distribution.

normal

The type of distribution shown in the graph below is a(n) _____ distribution.

normal

The parameter λ in an exponential distribution can be interpreted as a:

rate

A simulation model extends spreadsheet modeling by _____.

replacing the use of single values for parameters with a range of possible values

Which of the following does not represent a factor manager might consider when employing LP for production scheduling?

risk assessment

The _____ value for each less-than-or-equal-to constraint indicates the difference between the left-hand and right-hand values for a constraint.

slack

Suppose that EVPI=0. This means that

the decision problem involves no risk

A facility produces two products. The labor constraint (in hours) is formulated as: 350x1+300x2 ≤ 10,000. The number 10,000 represents

there are 10,000 hours of labor available for use.