A company produces 3 pound bags of trail mix using the following ingredients (cost per pound are indicated in parentheses: almonds ($2.50) peanuts ($1.50) pretzel sticks ($1) raisons ($2.15), dried apples ($1.40) dried cranberries ($2.75) There are 500 pounds of almonds available, 1500 pounds of peanuts available, 1800 pounds of pretzel sticks, 460 pounds of raisons, 400 pounds of dried apples, and 380 pounds of dried cranberries. The mix must contain at least 25% nuts (almonds and peanuts) and at most 40% pretzel sticks. Dried fruit must be at least 10% the mix and raisons must be at least 5% of the mix. The company has a contract to produce 1200 bags (so 3600 pounds total) for a Grocery chain. The company wants to minimize the cost of producing the trail mix. The company also wants to be able to easily modify the model such as to increase the 1200 bags to 1300 bags without having to modify a bunch of constraints. (so for example, for the maximum 40% pretzel sticks, do not just use X3<=1440 write the constraint in terms of the other variables) Create the required Linear Programming model, and solve using QM for Windows. Write a complete managerial report, using the format in your syllabus. In the results section, answer the following questions (please number your answers)

1. How many pounds of each ingredient should be used to minimize the total cost of producing 1200 bags of the mix, and what is the total cost?

2. How much of each ingredient do we have left over?

3. Are any of the reduced costs for any of the ingredients greater than 0? Interpret them.

4. If the company can increase the amount of only one ingredient availability, which should they increase? By how much? Explain using the dual prices.