Problem:
Minimization Problem - Simplex Method for a blending decision
The Corporation faces a blending decision in developing a new cat food. Two basic ingredients have been combined and tested, and the company has determined that to each can of cat food at least 30 units of protein and at least 80 units of riboflavin must be added. These two nutrients are available in two competing brands of animal food supplements. The cost per kilogram of the brand A supplement is $9, and the cost per kilogram of brand B supplement is $15. A kilogram of brand A added to each production batch of cat food provides a supplement of 1 unit of protein and 1 unit of riboflavin to each can. A kilogram of brand B provides 2 units of protein and 4 units of riboflavin in each can. The company must satisfy these minimum nutrient standards while keeping costs of supplements to a minimum.
a. Formulate this problem to find the best combination of the two supplements to meet the minimum requirements at the least cost.
b. Solve for the optimal solution by the simplex method.