XYZ Foods Inc. has a contract to produce 3000 pounds of trail mix for a convention. Ingredients available and cost per pound are peanuts ($2.50), raisons ($2.25), dried bananas ($1.50), dried cranberries ($3), and pretzel sticks ($1). There are 1000 pounds of peanuts available, 1400 pounds of pretzel sticks, 460 pounds of raisons, 400 pounds of bananas, and 500 pounds of cranberries.
The mix should contain at least 25% peanuts and at most 50% pretzel sticks. Bananas must be at least 10% the mix and raisons + cranberries must be at least 15% of the mix.
The company wants to minimize the cost of producing the 3000 pounds of trail mix. The company also wants to be able to easily modify the model - such as to increase the 3000 pounds to 3200 pounds without having to modify a bunch of constraints. (so for example, for the maximum 50% pretzel sticks, do not just use X5<=1500 - write the constraint in terms of the other variables)
Create the required Linear Programming model, and solve using Lingo. 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 3000 pounds of the mix, and what is the total cost?
2. Are any of the reduced costs for any of the ingredients greater than 0? Interpret.
3. If XYZ can increase the amount of ingredient availability, which should they try to increase? Explain using the dual prices.
4. If we could change one of the minimum or maximum percentage constraints, which would lower the cost of the mix the most? Explain using the dual prices.
Submission instructions:
You are to submit a single word document using the assignment link. Do not send me lingo files! Copy and paste your lingo output to an appendix. Your document will consist of
1. A managerial report - using the format in your syllabus
2. Appendix A - your Linear Programming model
Appendix B - your Lingo output