Category: Mathematics

Spreadsheet model

Posted on | by Brian Leakey
  1. The Wacker Company manufactures two types of lawn trimmers: an electric model and a gas model. The company has contracted to supply a national discount retail chain with a total of 25,000 electric trimmers and 20,000 gas trimmers. However, Wacker’s production capability is limited in three departments: production, assembly, and packaging. The following table summarizes the hours of processing time available and the processing time required by each department, for both types of trimmers: Hours Required per Trimmer Electric Gas Hours Available Production 0.20 0.40 10,000 Assembly 0.30 0.50 15,000 Packaging 0.10 0.10 5,000

The company makes its electric trimmer in-house for $55 and its gas trimmer for $85. Alternatively, it can buy electric and gas trimmers from another source for $67 and $95, respectively.

a. Develop a spreadsheet model to determine how many gas and electric trimmers the company should make and how many it should buy to fulfill its contract in the least costly manner.
Use a Sensitivity Report to answer the following:
b. If the cost to make gas trimmers increased to $90 per unit, how would the optimal solution change? Explain.
c. How much should the company be willing to pay to acquire additional capacity in the assembly area? Explain.
d. How much should the company be willing to pay to acquire additional capacity in the production area? Explain.
e. What will happen to total cost if the demand for electric trimmers increases by 1,000? Explain.

  1. The ELC Corporation manufactures two industrial-sized electrical devices: generators and alternators. Both of these products require wiring and testing during the assembly process. Each generator requires 4 hours of wiring and 2 hour of testing and can be sold for a $450 profit. Each alternator requires 6 hours of wiring and 1 hours of testing and can be sold for a $200 profit. There are 260 hours of wiring time and 140 hours of testing time available in the next production period and ELC wants to maximize profit.
    a. Formulate a spreadsheet model and use Solver to solve this LP problem. Copy and paste model below.
    b. Suppose the company can acquire additional wiring time at a very favorable cost. Should it do so? Why or why not?
    c. How much of a premium (above current costs) would the company be willing to spend to get an extra hour of testing time?

Theories and Models of Crisis Response

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Note: The Assignment is due by Day 4 prior to the Discussion.
To understand effective service delivery in response to critical incidents, helping professionals must first understand theories of how individuals process crisis and models for responding to survivors. For example, being aware of the Childhood Sexual Abuse Accommodation Syndrome can help sexual trauma practitioners conceptualize the cognitive processing of sexual abuse from the perspective of the child or adult survivor (Summit, 1992). Other theories include the eco-systemic theory (the effects of crisis affect more than just the survivor), the constructivist self-development theory (each individual constructs the meaning of his or her own traumatic event), and the resilience theory (the ability to recover from crisis events). Models provide techniques for working with crisis survivors, including but not limited to Psychological First Aid and suicide prevention models. Familiarity with theories and models related to crisis and crisis intervention provides important foundational knowledge that informs effective response to survivors.

For this Assignment, select three theories and/or response models that are used when working with survivors of critical incidents and that you think are particularly valuable.

The Assignment (2–3 pages):

Briefly describe each of the theories/models you selected.
For each, explain its value in helping individual(s) who have experienced or are experiencing crisis, trauma, or disaster. Be specific and provide examples to illustrate your points.

The projectile

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Dawson kicked a football from the ground and it followed the projectile h(t)=-15t^2+150t where t is the time in seconds, and h is the height of the ball in feet. Answer the following questions about the scenario:
How long was the ball in the air when it was at its maximum height? Round to two decimal
places if needed.
b) What is the maximum height the ball reached? Round to two decimal places if needed.
c) How long was the ball in the air? Round to two decimal places if needed.

Pythagorean Theorem

Posted on | by Brian Leakey

In the 1939 movie The Wizard of Oz, upon being presented with a Th.D. (Doctor of Thinkology), the Scarecrow proudly exclaims, “The sum of the square roots of any two sides of an isosceles triangle is equal to the square root of the remaining side.” Did the Scarecrow get the Pythagorean Theorem right? In particular, describe the four errors in the Scarecrow’s statement.

2- Measures of Central Tendency
A student’s parents promise to pay for next semester’s tuition if an A average is earned in math. With examination grades of 97%, 97%, 75%, 70%, and 55%, the student reports that an A average has been earned. Which measure of central tendency is the student reporting as the average? How is this student misrepresenting the course performance with statistics?

The constant of proportionality

Posted on | by Brian Leakey

The required cooling capacity in BTUs for an air conditioner is proportional to the area of the room being cooled. A room of 275 square feet requires an air conditioner whose cooling capacity is 5500 BTUs.
a) What is the constant of proportionality? (Round to two decimal places if necessary.)
b) If an air conditioner has a cooling capacity of 13,000 BTUs, how large a room can it cool?
What I Did Mathematically? Why I Did It – Explain Why

The constant of proportionality

Posted on | by Brian Leakey

The required cooling capacity in BTUs for an air conditioner is proportional to the area of the room being cooled. A room of 275 square feet requires an air conditioner whose cooling capacity is 5500 BTUs.
a) What is the constant of proportionality? (Round to two decimal places if necessary.)
b) If an air conditioner has a cooling capacity of 13,000 BTUs, how large a room can it cool?
What I Did Mathematically? Why I Did It – Explain Why

Price demand equation and the total cost function

Posted on | by Brian Leakey

Problem: The price demand equation and the total cost function for the weekly production of Toyota Cars, are given by
X = 100 — P and C(X) = x^3/100 + 30X
Where X stands for the quantity of cars produced and P for the unit price.
Part I: The aim of this part is to use the course technical skills in optimization to determine the optimal quantity produced, the optimal price and the maximum profit. Please show all calculations you have done with steps labeling each calculation like the critical values
Part II: Using the graphing strategy, show the graph of the profit function showing the maximum profit. All graphs will have x as the horizontal. The graph must be supported by the graphing strategy calculations you have done, this includes, the classification of all turning points, the intercepts and the domain of the problem.
Instruction: You must submit a full solution of the problem properly typed (or clearly handwritten) and a total of two graphs with proper labels and relevant information must be tagged properly like the breakeven point and any maxima/minima. I