**Problem 1(50 Points)**

Print Media Advertising (PMA) has been given a contract to market Buzz Cola via newspaper ads in a major Southern newspaper. Full-page ads in the weekday editions (Monday through Saturday) cost $2000 per day, whereas on Sunday a full-page ad costs $8000. Daily circulation of the newspaper is 30,000 on weekdays and 80,000 on Sunday.

PMA has been given a $40,000 advertising budget for the month of August. The experienced advertising executives at PMA feel that both weekday and Sunday newspaper ads are important; hence, they wish to run the equivalent of at least eight weekday and at least two Sunday ads during August. (Assume that a fraction of ad would simply mean that a smaller ad is placed on one of the days; that is, 3.5 ads would mean three full-page ads and one one-half page ad. Also assume that smaller ads reduce exposure and cost proportionately.) This August has 26 weekdays and 5 Sundays.

If the objective is to maximize cumulative total exposure (as measured by circulation) for the month of August, answer the following questions:

a) **(20 Points)**Write the linear programming model for this problem. Define the variables precisely. (** Hint**: PMA is deciding how to advertise in a major newspaper.)

b) **(20 Points)**Find the optimal solution using the graphical method. Show all steps. Find the points of intersection algebraically.

**c) ****(10 Points)**Find the optimal solution using Excel Solver. Copy and paste the Excel spreadsheet and the Answer Report.** Problem 2(50 Points)**

Missouri Mineral Products (MMP) purchases two unprocessed ores from Bolivia Mining, which it uses in the production of various compounds. Its current needs are for 800 pounds of copper, 600 pounds of zinc, and 500 pounds of iron. The amount of each mineral found in ** each 100 pounds** of the unprocessed ores and MMP’s cost

Ore |
Copper |
Zinc |
Iron |
Waste |
Cost |

La Paz ore |
20 |
20 |
20 |
40 |
$100 |

Sucre ore |
40 |
25 |
10 |
25 |
$140 |

Suppose the objective is to minimize the total purchasing costs, answer the following questions:

a) **(20 Points)**Write the linear programming model for this problem. Define the variables precisely. (** Hint**: MMP is deciding how many of each type of ore to buy in order to extract enough minerals to satisfy its customers.)

b) **(20 Points)**Find the optimal solution using the graphical method. Show all steps. Find the points of intersection algebraically.

c) **(10 Points)**Find the optimal solution using Excel Solver. Copy and paste the Excel spreadsheet and the Answer Report.

Answer the following two questions using the sensitivity report!

d) **(Bonus 5 Points)**what happen to the optimal decision and optimal cost if the price for La Paz ore increases to $110 per 100 pounds?

e) **(Bonus 5 Points) **what happento the optimal decision and optimal cost if the demand for iron increased from 500 pounds to 550 pounds?

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