(Animal feed mix problem) The Battery Park Stable feeds and houses the horses used to pull tourist-filled carriages through the streets of Charleston's historic waterfront area. The stable owner, an ex-racehorse trainer, recognizes the need to set a nutritional diet for the horses in his care. At the same time, he would like to keep the overall daily cost of feed to a minimum. The feed mixes available for the horses' diet are an oat product, a highly enriched grain, and a mineral product. Each of these mixes contains a certain amount of five ingredients needed daily to keep the average horse healthy. The table on this page shows these minimum requirements, units of each ingredient per pound of feed mix, and costs for the three mixes. In addition, the stable owner is aware that an overfed horse is a sluggish worker. Consequently, he determines that 6 pounds of feed per day are the most that any horse needs to function properly. Formulate this problem and solve for the optimal daily mix of the three feeds.
FEED MIX
DIET OAT ENRICHED MINERAL MINIMUM DAILY
REQUIREMENT PRODUCT GRAIN PRODUCT REQUIREMENT
(INGREDIENTS) (UNITS/LB) (UNITS/LB) (UNITS/LB) (UNITS)
A 2 3 1 6
B 0.5 1 0.5 2
C 3 5 6 9
D 1 1.5 2 8
E 0.5 0.5 1.5 5
Cost/lb $0.09 $0.14 $0.17