What are the decision variables, Basic Statistics

Question 1

Water resources in many parts of Australia are being closely watched and restrictions have been imposed on activities such as garden watering. Suppose that SA Water monitors water usage in an Adelaide suburb and finds that for one summer the average household usage is 408 litres per day. A year later it examines records for a randomly selected sample of 50 households and finds that there is a daily mean usage of 380 litres with a standard deviation of 25 litres.

(a) Construct and interpret a 95% confidence interval for the population mean daily water usage in the second summer. Does the population have to be Normal here? Explain.

(b) Do you think water usage has changed in the second summer? Explain.

Question 2

David, Diana and Lydia are the sole partners and workers in a company that produces fine clocks. David and Diana are each available to work a maximum of 40 hours per week at the company, while Lydia is available to work a maximum of 20 hours per week.

The company makes two different types of clocks: a grandfather clock and a wall clock. To make a clock, David (a mechanical engineer) assembles the inside mechanical parts of the clock while Diana (a woodworker) produces the hand carved wood casings. Lydia is responsible for taking orders and shipping the clocks. The amount of time required for each of these tasks is shown below.

1765_table task.png

Each grandfather clock built and shipped yields a profit of $300, while each wall clock yields a profit of $200.

The three partners now want to determine how many clocks of each type should be produced per week to maximize the total profit using linear programming. They have asked for your help.

(a) Formulate a linear programming model for this problem. In doing so, consider the following:

1. What are the decision variables for this problem?

2. What is the objective for this problem? Using your decision variables, formulate the objective function.

3. What are the constraints in this problem? Using your decision variables, formulate these constraints.

(b) Use EXCEL Solver to obtain a solution to the linear programming problem from part (a), together with an Answer Report and a Sensitivity Report. Provide a copy of your EXCEL spreadsheet and of the two Excel reports in your assignment submission.

EXCEL Instructions: All EXCEL output should bear your ID number.

Your inserted output should be titled 'FamilyName,GivenName,ID'

Please refer to Topic 5 in the Excel Booklet or the Linear Programming Supplement to the textbook (pdf file posted on the course resources website) for detailed instructions on how to set up your spreadsheet and use Solver. You may use the Excel file on the portal as a template.

(c) Grandfather clocks have become very popular and the partners feel that a unit profit per grandfather clock of $375 may be possible. Would the solution obtained in part

(b) still be optimal? Which of the EXCEL reports helps you answer this question? Justify your answer carefully. How would the total profit change, if at all?

(d) Prepare a report that summarizes your linear programming results. Your report should discuss the following:

1. The optimal number of grandfather and wall clocks, as well as the maximum total profit.

2. Resulting work hours for each of the partners. How do these compare to the maximum hours each partner is able to allocate to this business?

3. Profit per unit considerations from part (c).

Report Instructions: Your report should be at most one page, in 12pt Times New Roman or a similar font, with 1.5 line spacing and at least 2cm margins.

Posted Date: 2/25/2013 4:32:21 AM | Location : United States







Related Discussions:- What are the decision variables, Assignment Help, Ask Question on What are the decision variables, Get Answer, Expert's Help, What are the decision variables Discussions

Write discussion on What are the decision variables
Your posts are moderated
Related Questions
You notice at the gym that it appears more women tend to work out together, while more men tend to work out alone.  To show whether this difference is significant, you collect data

If today is a weekday and it’s not a holiday, then you go to work. However, if it’s a weekday and a holiday, then what you do depends on the weather: If it’s raining, you play vide

What are the steps in a recruitment process and who are responsible for each step?

SPSS Assignment 1. Execute the following functions using SPSS.  a) Enter the following data Case Age Weight Gender

what is the Texas state gemstone

Conceptual Structure has also resolved several issues which were uncertain by sales expectations for some time. Activities and dealings that can't be worked by designed financial s


Use the given information to find the number of degrees of? freedom, the critical values chi Subscript Upper L Superscript 2?2L and chi Subscript Upper R Superscript 2?2R?, and the

Assume that the pulleys are small frictionless pulleys. Three weights are supported as shown and have weights of W A = P5 N, W B = P6 N, and W C = P7 N.  Determine angle θ

1. If each sample taken has 500 units, and the average proportion nonconforming is 0.034, what is the upper and lower control limits for the p-chart? 2. If you sample 450 parts