Bogusburgers, Inc., is a California company which produces a hamburger mixture of ground beef, soybeans and corn, which it sells as a cheaper substitute for pure ground beef. Presently the company is evaluating the composition of its product and its transportation network.

Ground beef is purchased from Thousand Oaks, and the supplier can sell up to 3300 pounds per day to Bogusburgers at the price of $2.40 per pound. Up to 3000 pounds of soybeans can be purchased per day at a price of $0.50 per pound from Fresno. Up to 2700 pounds of corn per day is available from Bakersfield at $0.30 per pound.

Processing plants are located at Sacramento, San Jose, and San Bernadino. At these plants the ingredients are combined in a rather simple process which involves no net change in weight. From the processing plants the mixture is shipped to distribution centers in Reno, San Francisco, Las Vegas and San Diego. Processing capacities per day at 1500 pounds at Sacramento, 2500 Pounds at San Jose, and 2000 pounds at San Bernadino. Quantities demanded at the distribution centers per day are 1000 pounds at Reno, 2500 pounds at San Francisco, 1500 pounds at Las Vegas and 2000 pounds at San Diego.

The composition of the product must meet certain standards. First, for taste requirements the company has a policy of using at least 40% beef in the mixture. Water content must be no more than 50%, fat content must be no more than 20%, carbohydrate content must be no more than 25%, and protein content must be at least 20%.

The table below shows the composition of the three ingredients:

Water Fat Carb Protein

Beef 55% 28% 0% 16%

Soybeans 9% 7% 35% 45%

Corn 39% 0% 50% 11%

Please answer the following questions in words and support your answers with all relevant work, calculation, and computer printouts.

1. Formulate (including definition of the variables) and solve the problem determining the cheapest mix of ingredients that will meet all of the requirements. What is the cost per pound?
   (hint: there are 9 constraints: 3 supply constraints, 1 taste constraint, 4 composition constraints and 1 constraint for the total # of pounds produced)
2. If you could increase the supply of any one of the three ingredients, which one would you increase and how much would the new supply be?
3. If you could relax any one of the water, fat, carbohydrate or protein requirements, which one would you relax and what would the new requirement be?
4. Shipping costs are proportional to the highway miles between cities. Find the distances from processing plants to distributors. Show your source.
5. Use the mileages you have obtained (without rounding) to determine the optimal daily flows from processing plants to distributors.
6. From your answers to parts 1 and 5 above, show the daily flows from suppliers to processing plants and from processing plants to distribution centers.

Price: $10.96

Solution: The downloadable solution consists of 5 pages, 596 words.
Deliverable: Word Document