There are 100 cows in a ranch. The owner seeks to determine the amounts of cattle feed to buy so that minimum nutritional standards are satisfied, and at the same time total feed costs are minimised. The feed mix can be made up of the three grains that contain the following ingredients per kilogram (kg) of feed. The cost per kg of stocks X, Y, and Z are $2.00, $4.00, and $2.50 respectively. The minimum requirement per cow is 4 kg of ingredient A, 5 kg of ingredient B, 1 kg of ingredient C, and 8 kg of ingredient D. The ranch faces one additional restriction: it can only obtain 5kg of stock Z per cow from the feed supplier. Derive the decision variable(s), objective function(s), and constraint(s). Remember to state clearly what each variable represents. Setup the linear programming (LP) problem in standard form.

Feed (kg) Ingredient Stock X Stock Y Stock Z A 2 4 B C O 2 D