Problem  1 – include all steps

 

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 both the graphical method and Excel to find the optimal solution. ( I attached powerpoint presentation to show lp model graph method and excel)

 

 

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

include all steps to reach solution

 

(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 in a table format using the Mean Absolute Deviation (MAD).

 

 

Problem  3

include all steps to reach solution

 

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?