TRUE/FALSE – clearly indicate your response.
1. Sensitivity analysis is the analysis of the effect of parameter changes on the optimal solution.T .

2. The sensitivity range for an objective function coefficient is the range of values over which the current optimal solution (product mix) will remain optimal. T .

3. The sensitivity range for a right-hand-side value in a constraint is the range of values over which the quantity values can change without changing the solution variable mix, including slack variables. T .

4. The terms reduced cost, shadow price, and dual price all mean the same thing. F .

5. Sensitivity analysis can be used to determine the effect on the solution for changing several parameters at once. F .

6. A negative shadow price indicates that the objective function decreases when the right hand side of a constraint increases. T .

7. For a profit maximization problem, if the allowable increase for a coefficient in the objective function is infinite, then profits are unbounded. T .

MULTIPLE CHOICE – clearly indicate your response.
1. For a linear programming problem, assume that a given resource has not been fully used. In other words, the slack value associated with that resource constraint is positive. We can conclude that the shadow price associated with that constraint: A. will have a positive value.

B. will have a negative value.
C. will have a value of zero.
D. could have positive, negative, or zero value.D .

Use the following information for problems 2 – 5:
Aunt Anastasia operates a small business; she produces seasonal ceramic objects to sell to tourists. For the spring, she is planning on make baskets, eggs, and rabbits. Based on your discussion with your aunt you...

...Article Review 1
DeGeorge, B., Santoro, A. (2004). “Manipulatives: A Hands-On Approach to Math.” Principal, 84 (2), (28-28).
This article speaks about the importance and significance of the use of manipulatives in the classroom, specifically in the subject of math. Manipulatives have proven to be valuable when used in a math class and are even more valuable to the children when they are young, and are learning new math concepts. Students are able to physically visualize the math concepts and gain knowledge because they understand what they’re learning a whole lot better and they also are able to gain insights on those concepts. Different examples of manipulatives may include counting with beans or M&M’s, using pattern blocks, puzzles, tangrams, and flash cards, just to name a few.
Using manipulatives in a math class are beneficial to both the student and the teacher because the teacher is able to explain the concepts to the students in a much easier manner using the hands-on technique, rather than explaining it verbally. It’s especially beneficial to the student because by incorporating these manipulatives into their learning process, they are able to pick up the concepts much quicker and in a way that they better understand, yet are having fun while doing it. When they have the concepts down, the students’ self-esteem goes up and they feel encouraged to keep on going.
After...

...Introduction to Management Science, 11e (Taylor)
Chapter 1 Management Science
1) Management science involves the philosophy of approaching a problem in a subjective manner.
Answer: FALSE
Diff: 1 Page Ref: 2
Section Heading: The Management Science Approach to Problem Solving
Keywords: scientific approach
AACSB: Analytic skills
2) Management science techniques can be applied only to business and military organizations.
Answer: FALSE
Diff: 1 Page Ref: 2
Section Heading: The Management Science Approach to Problem Solving
Keywords: scientific approach, problem solving
AACSB: Analytic skills
3) Management scientists use the terms "data" and "information" interchangeably--that is, the two terms mean the same thing
Answer: FALSE
Diff: 2 Page Ref: 4
Section Heading: The Management Science Approach to Problem Solving
Keywords: data
AACSB: Analytic skills
4) A management science solution can be either a recommended decision or information that helps a manager make a decision
Answer: TRUE
Diff: 2 Page Ref: 5
Section Heading: The Management Science Approach to Problem Solving
Keywords: model, management science techniques
AACSB: Analytic skills
5) A variable is a value that is usually a coefficient of a parameter in an equation.
Answer: FALSE
Diff: 1 Page Ref: 3
Section Heading: The Management Science Approach to Problem Solving
Keywords: variable
AACSB: Analytic skills
6) Parameters are known,...

...
ANALYSIS
Physics has a lot of topics to cover. In the previous experiments, we discussed Forces, Kinematics, and Motions. In this experiment, the focus is all about Friction. Friction is the force resisting the relative motion of solid surfaces, fluid layers, and material elements sliding against each other. There are several types of friction like fluid friction which describes the friction between layers of a viscous fluid that are moving relative to each other; dry friction which resists relative lateral motion of two solid surfaces in contact and is subdivided into static friction between non-moving surfaces, and kinetic friction between moving surfaces; lubricated friction which is a case of fluid friction where a fluid separates two solid surfaces; skin friction which is a component of drag, the force resisting the motion of a fluid across the surface of a body; internal friction is the force resisting motion between the elements making up a solid material while it undergoes deformation and sliding friction.
When surfaces in contact move relative to each other, the friction between the two surfaces converts kinetic energy into heat. This property can have dramatic consequences, as illustrated by the use of friction created by rubbing pieces of wood together to start a fire. Kinetic energy is converted to heat whenever motion with friction occurs, for example when a viscous fluid is stirred. Another important consequence of many types of friction can be wear,...

...
The case between Beauty and Stylish involves concept of a valid contract, pre-contractual statements, express term and misrepresentation.
A valid contract is established between Beauty and Stylish when an offer is accepted and there is intention for both parties to create legal relations. An offer refers to the expression of willingness of the offerer to be contractually bound by an agreement if his or her offer is properly accepted. It has to be clear and certain in terms. It must also be communicated to the offeree before it is being accepted. In addition, the acceptance has to be unqualified, unconditional and made by a positive act. In the case of Beauty and Stylish, a positive act refers to the signing of the contract. All terms of the offer must be accepted without any changes and cannot be subjected to any condition, taking effect only upon fulfillment of that condition. When Beauty and Stylish enter into the agreement, they must intend to bind and bound legally to each other by their agreement. This is the intention to create legal relations between two parties. In the meanwhile, this contract must possess consideration. A contract must therefore be a two-sided affair, with each side providing or promising to provide something of value in exchange for what the other is to provide.
Every contract, whether oral or written, contain terms. The terms of a contract set out the rights and duties of the parties. Terms are the promises and undertakings given by each...

...Week 9 Quiz 5:
1. In a _______ integer model, some solution values for decision variables are integer and others can be non-integer.
a. total
b. 0 – 1
c. mixed
d. all of the above
2. In a total integer model, some solution values for decision variables are integer and others can be non-integer. TRUE/FALSE
3. In a problem involving capital budgeting applications, the 0-1 variables designate the acceptance or rejection of the different projects. TRUE/FALSE
4. If a maximization linear programming problem consist of all less-than-or-equal-to constraints with all positive coefficients and the objective function consists of all positive objective function coefficients, then rounding down the linear programming optimal solution values of the decision variables will ______ result in a(n) _____ solution to the integer linear programming problem.
A) always, optimal
B) always, non-optimal
C) never, non-optimal
D) sometimes, optimal
E) never, optimal
5. The branch and bound method of solving linear integer programming problems is an enumeration method. TRUE/FALSE
6. In a mixed integer model, all decision variables have integer solution values.
TRUE/FALSE
7. For a maximization integer linear programming problem, feasible solution is ensured by rounding _______ non-integer solution values if all of the constraints are less-than -or equal- to type.
A) up and down
B) up
C) down
D) up or down
8. In a total integer model,...

...Final Examination
Math540 Quantitative Methods
Good luck on the exam. I hope you have enjoyed the course. Dr. West
Multiple Choice (2 points each) (Select 8 – drop 1)
______1) For your project, what one way will not possibly generate increased profit?
a) Increase your building space or lot size.
b) Decrease the money paid to employees.
c) Refinance the loan at a lower rate.
d) Charge more for your services.
_____ 2) Which of the following is a valid objective function in linear programming?
a) Max 5xy.
b) Min 4x + 5y - (2/3)z.
c) Max 4 x 2 + 6 Y 2.
d) Min (x + y) / z.
e) None of the above.
______3) The improvement in the value of the objective function per unit increase in a right-hand side is the
a. sensitivity value.
b. shadow price.
c. constraint coefficient.
d. slack value.
_____4) Study of how changes in the coefficients of a linear programming problem affect the optimal solution is called
a. sensitivity analysis.
b. transshipment analysis.
c. sunk cost analysis.
d. duality analysis.
e. none of the above.
_____5) Which of these is not a type of integer model?
a. a...

...Yr 10
Mathematics
Assignment
LCR Maths
By Adonis Chigeza
Understanding and Fluency Tasks
Task A
1. y = 1.2𝑥 + 2.57
2. Interpolation: y = -3.43
Extrapolation: y = -8.23
Task B
a) The equation for the path of the ball is h = -0.1t^2 + 0.9t + 1 (h = height, t = time)
b) The vertical height of the ball after 2. seconds2.664m
c) The maximum height reached by the ball is 3.025m
d) The time of with the ball is at maximum height of 3.025 is 4.5 seconds
e) The total time in which the ball was in the air is 10 seconds
f) The two times in which the ball was 1 metre above ground is 0 and 9
Adonis Chigeza 10C
LCR Mathematics
Problem Solving and Reasoning Task
1.
Equation: y = -1.2𝒙2 + 8.4𝒙
a. The bridge is 7 metres wides so therefore it will successfully span the river with 2
metres to spare.
b. If a yacht has a 15 metre mask it will be unable to pass safely under the bridge
because the bridge only has a vertical height 14.7 metres.
Adonis Chigeza 10C
LCR Mathematics
2. Equation: v= -0.2h2 + 2.4h
a. The horizontal distance covered by the rocket when it reached its maximum
height of 7.2 metres was 6 metres.
b. The maximum height reached by the rocket was 7.2 metres.
c. At the horizontal distance of 9 metres from the launch site, there is a 5.2 metre
wall and at that vertical distance, the rocket has a vertical distance 5.4 metre.
That is not taking to account the dimensions of the rocket, however the rocket
cannot have...

...• What were the most revolutionary social and economic developments of the last quarter of the nineteenth century?
• How did different groups of Americans respond to those changes and how effective were their responses?
• What role did government play in these developments?
In the late 1900s some of the most social and economic developments were railroads, steel oil, the type writer cash register, light bulb and agriculture. The development of the railroad made it easier for immigrant to come to this country for work. This meant that there were more group of different races and cultures in America. And in some states there became an over population and city workers like police and garbage men could not keep up with the demand of so many people. Some groups mover to open land for the Homestead Act. They had hope of farming and staying on the land for at least five years as agreed but the supply and demand of agriculture did sustain so many farmer moved off the land well before their five years. The government played many different role I deescalating some issues in American history. Women and children were being worked for long hours and getting paid a little bit of nothing in return for their hard work. So the government put labor laws into place that were to protect women and children. As oil, steel and railroad industries grew so did the levels of pollution. The government again put laws that were to protect animals and the earth so that there would not...