Analytics Final (Exam 2 Review)
(SA) When the objective function can increase without ever contacting a constraint the LP, we call such solution:
Unbounded solution
How many constraints are there in a transshipment problem which has n nodes and m arcs?
n
An oil company wants to create lube oil, gasoline and diesel fuel at two refineries. There are two sources of crude oil. Consider arc 204. The per unit shopping cost of crude B from source 2 (node 2) to refinery 2 (node 4) is $11 and the yield is 85 percent. The following network representation depicts this problem. What is the balance of flow constraint for node 3? (Refinery 1)?
.80x13 + .95X23 - X35 - X36 - X37 = 0
An oil company wants to create lube oil, gasoline and diesel fuel at two refineries. There are two sources of crude oil. Consider arc 204. The per unit shopping cost of crude B from source 2 (node 2) to refinery 2 (node 4) is $11 and the yield is 85 percent. The following network representation depicts this problem. What is the balance of flow constraint for node 7? (Diesel)?
.90X37 + .95X47 = 75
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, 45 minutes in sanding, and 1 hour in finishing. In the coming weel 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. he optimal solution is the intersection of:
1D + 0.5W <= 40 and 0.5D + 0.75W <= 40
The following linear programming problem has been written to plan the production of two products. The company wants to maximize its profits X1 = number of product 1 produced in each batch X2 = number of product 2 produced in in each batch MAX: 150x1 + 250x2 S.T.2X1 + 5x2 <= 200 - resource1 3x1 + 7x2 <= 175 - resource2 X1,X2 >= 0 How many units of resource 1 are consumed by each unit of product 1 produced?
2
What is the correct Analytic Solver Platform function for generating random numbers from the following distribution on the number of children in families?
=PsiDiscrete(A2:A6,B2:B6)
The owner of Fix-a-dent Auto Repair wants to study the growth of his business using simulation. He is interested in simulating a number of damaged cars and the amount of damage to the cars each month. He currently repairs 100 cars per month and feels this can vary uniformly between a decrease of as much as 3% and an increase of up to 5% (average change of %1) over the previous months. The dollar value of the damage to the cars is a normally distributed random variable with a mean of $3,000 and a standard deviation of $500. The average repair bill has been increasing steadily over the years and the owner expects the mean repair bill will increase by 1% per month. You have created the following spreadsheet to simulate the problem: Which Excel function should go in cell C8 and copied to cells C9:C18 to compute the average dmanage per car in the month?
=PsiNormal($C$3*(1+$F$3)^A8, $H$3)
The owner of Fix-a-dent Auto Repair wants to study the growth of his business using simulation. He is interested in simulating a number of damaged cars and the amount of damage to the cars each month. He currently repairs 100 cars per month and feels this can vary uniformly between a decrease of as much as 3% and an increase of up to 5% (average change of %1) over the previous months. The dollar value of the damage to the cars is a normally distributed random variable with a mean of $3,000 and a standard deviation of $500. The average repair bill has been increasing steadily over the years and the owner expects the mean repair bill will increase by 1% per month. You have created the following spreadsheet to simulate the problem: Which Excel function should go in cell B8 to compute the number of cars repaired in the first month?
=PsiUniform($C$2*(1-$F$2), $C$2*(1+$H$2))
(SA) _____________ indicate connections, routes, or paths in a network. In network flow problems, decision variables are represented by __________. What is _______?
Arcs
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, 45 minutes in sanding, and 1 hour in finishing. In the coming weel 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. Consider the feasible region shown in the provided diagrams. Select the correct diagram that has each equation in part a to the corresponding line in the diagram
B
Agri-Pro is a company that sells agricultural products to farmers in a number of states. They offer custom feed mixing, in which a farmer can order a specific amount of livestock feed and specify the amount of corn, grain, and minerals the feed should contains. Agri-Pro has received an order for 10,000 pounds of chicken feed to be mixed from the following feeds. The order must contain at least 15% corn, 15% grain, and 20% minerals. In this problem, we rescaled the objective function and constraints because scaling problems:
D - all of these choices are correct Can cause problems in accuracy of solutions returned Can cause Analytic Solver Platform to consider a linear problem as nonlinear Are caused by small numbers and large numbers used in the same problem
As the number of replicates in a simulation increases the width of a confidence interval computed from the simulation results.
Decrease
The following diagram shows the constraints for a LP model. Assume the point (0,0) satisfies constraints (B,J) but does not satisfy constraints (D,H) or (C,I). Which set of points on this diagram defines the feasible?
I, F, G, J
In a transshipment problem, which of the following statements is a correct representation of the balance-of-flow rule of Total Supply < Total Demand?
Inflow - Outflow <= Supply or Demand
What does the Excel "=SUMPRODUCT(A1:A5,C6;C10)" function do?
Multiplies each pair of cells in two arrays matched by position and sum the products
(SA) What is the name of this variable? - A spreadsheet input cell containing a random number generator - Any variable whose value cannot be predicted with certainty - The outcome of a simulation model
Random variable
PCA Flight 343 flies between a small regional airport and a major hub. The plane has 19 seats & several are often vacant. Tickets cost $200 per seat and there is a 0.10 probability of a sold seat being vacant. If PCA overbooks, it must pay an average of $350 for any passengers that get "bumped". Demand for seats is random, as follows: As a successful data analyst, you would like to find the number of reservations that PCA Flight should accept. To do so, you run 7 simulations with 1000 trials each. Each simulation assumed the accepted reservation varying from 19 to 25 seats. After running the simulation, you plotted the result from the simulation: Which of the following statements is true?/
The minimum marginal profit is the same across the simulations because that is when the minimum demand for seat takes place.
Why do we use random number seeds?
To evaluate different values for the controllable parameter
Agri-Pro is a company that sells agricultural products to farmers in a number of states. They offer custom feed mixing, in which a farmer can order a specific amount of livestock feed and specify the amount of corn, grain, and minerals the feed should contains. Agri-Pro has received an order for 10,000 pounds of chicken feed to be mixed from the following feeds. The order must contain at least 15% corn, 15% grain, and 20% minerals. Which of the following statement is incorrect?
We set F6 <= G6 as a constraint
When do alternate optimal solutions occur in LP models?
When a binding constraint is parallel to a level curve
A production optimization problem has 4 decision variables and resource 1 limits how many of the 4 products can be produced. Which of the following constraints reflects this fact?
f (X1, X2, X3, X4) <= b1
Which of the following is the general format of an objective function?
f (X1, X2,...,Xn)
A set of values for the decision variables that satisfy all the constraints and yields the best objective function value is:
An optimal solution
What are the three common elements of an optimization problem?
Decisions, constraints, an objective
