32 A boarding stable feeds and houses work horses used to pull tourist-filled carriages through the streets of a historic city. The stable owner wishes to strike a balance between a healthy nutritional standard for the horses and the daily cost of feed.

This type of horse must consume exactly 5 pounds of feed per day. The feed mixes available are an oat product, a highly enriched grain, and a mineral product. Each of these mixes contains a predictable amount of five ingredients needed daily to keep the average horse healthy. The table at the bottom of this page shows these minimum requirements, units of each nutrient per pound of feed mix, and costs for the three mixes.

Formulate this problem and solve for the optimal daily mix of the three feeds.

FEED MIX NEEDED (units/day)
NUTRIENT OAT (units/lb.)
GRAIN (units/lb.)
MINERAL (units/lb.)
A 2.0 3.0 1.0 6 B 0.5 1.0 0.5 2 C 3.0 5.0 6.0 9 D 1.0 1.5 2.0 8 E 0.5 0.5 1.5 5 Cost/lb. $0.33 $0.44 $0.57