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 3day moving average method for forecasting days 47.
(b) Use the 3day weighted moving average method for forecasting days 47. 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 – x^{2}
C(x) = 21 + 2x
a) Determine the profit function P(x).
b) Compute the breakeven quantities.
c) Determine the average cost at the breakeven 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 payoff 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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