An animal food must provide 60 units of vitamins and 65 calories per serving. One gram of soybean meal provides 2.5 units of vitamins and 5 calories. One gram of meat byproducts provides 4.5 units of vitamins and 3 calories. One gram of grain provides 5 units of vitamins and 10 calories. A gram of soybean meal costs 8¢, a gram of meat byproducts 9¢, and a gram of grain 10¢.
(a) What mixture of these three ingredients will provide the required vitamins and calories at minimum cost?
(b) What is the minimum cost?
x1 x2 s1 s2 s3 z
2.5 5 1 0 0 0 __
4.5 3 0 1 0 0 __
5 10 0 0 1 0 10
__ __ 0 0 0 1 0
There is more than one optimal basic solution to this problem. The answer depends on whether the tie in the minimum ratio rule is broken by pivoting on the second row or third row of the dual.
When pivoting on the second row of the dual, the mixture would contain __ grams of soybean meal, __ grams of meat byproducts, and __ grams of grain. When pivoting on the third row of the dual, the mixture would contain __ grams of soybean meal, __ grams of meat byproducts, and __ grams of grain.
The minimum cost is $__