Problem

Cattle are sent to a feedlot to be grain-fed before being processed into beef. The owners of a feedlot seek to determine the amounts of cattle feed to buy so that minimum nutritional standards are satisfied to ensure proper weight gain, while total feed costs are minimized. The feed mix used is made up of three grains that contain the following nutrients per pound of feed:

Feed mixes X, Y, and Z cost $3, $4, and $2.25 per pound, respectively. The minimum requirement per cattle per day is 4 pounds of nutrient A, 5 pounds of nutrient B, 1 pound of nutrient C, and 8 pounds of nutrient D. The ranch faces one additional restriction: it can only obtain 500 pounds of feed mix Z per day from the feed supplier regardless of its need. Because there are usually 100 cattle at the feed lot at any given time, this means that no more than 5 pounds of stock Z can be counted on for use in the feed of each cattle per day. Formulate this problem as a linear program and solve it by using Excel.