Project #11167 - quantative analysis

Please use word equation tool or excel drawing chart/graph tool if necessary. Problems must be complete and easy to understand.

Problem 1

The average prices for a product in twelve stores in a city are shown below.

\$1.99, \$1.85, \$1.25, \$2.55, \$2.00, \$1.99, \$1.76, \$2.50, \$2.20, \$1.85, \$2.75, \$2.85

Test the hypothesis that the average price is higher than \$1.87. Use level of significance a = 0.05.

Problem 2

Last week’s sales of a product at a retail store are shown in the following table:

 Day Sales (Dollars) 1 200 2 250 3 180 4 190 5 175 6 170 7 180

(a)    Use the 3-day moving average method for forecasting days 4-7.

(b)     Use the 3-day weighted moving average method for forecasting days 4-7. Use Weight 1 day ago = 4, Weight 2 days ago = 3, and Weight 3 days ago = 2.

(c)     Compare the techniques using the Mean Absolute Deviation (MAD).

Problem 3

The revenue and cost functions for producing and selling quantity x for a certain company are given below.

R(x) = 12x – x2

C(x) = 21 + 2x

a)      Determine the profit function P(x).

b)       Compute the break-even quantities.

c)       Determine the average cost at the break-even quantities.

d)       Determine the marginal revenue R’(x).

e)       Determine the marginal cost C’(x).

f)        At what quantity is the profit maximized?

Problem 4

A small winery manufactures 2 types of wine, Burbo's Better (X) and Burbo's Best (Y).  Burbo's Better results in profit of \$4 per quart, whereas Burbo's Best has profit of \$5 per quart. Two production workers mix the 2 wines. It takes a production worker 2 hours to mix a quart of the Better and 3 hours to mix a quart of the Best. Each worker puts in a 9 hour day. The quantity of alcohol than can be used to fortify the wine is limited to 24 ounces daily. Six ounces of alcohol are added to each quart of Burbo's Better and 3 ounces are added to Burbo's Best. Give the LP Model and use the graphical method to find the optimal solution.

Problem 5

A company purchases its merchandise for \$10 and sells for each item for \$20. The pay-off table for the problem is given below.

 Demand for Item Alternative Low Medium High Do nothing 0 0 0 Order Low 30,000 30,000 30,000 Order Medium 10,000 50,000 40,000 Order High -10,000 40,000 80,000 Probability 0.3 0.3 0.4

What is the decision based on each of the following criteria?

(a)    EMV approach

(b)   EOL approach

 Subject Mathematics Due By (Pacific Time) 08/26/2013 08:00 pm
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