Mane Event Stables is a horse boarding facility. Each month they are faced with varying needs terms of nutritional requirements of the horses they are boarding. They also face variable availablity of mixers that they use to make the feed for the horses. Below are the data on four different mixers that they will use to make the feed for the horses they are boarding this month. (the fourth mixer is actually “pure” vitamin C.)
Protein Fat Vitamin C $/pound Lbs. Available
Mixer 1 29% 8% 2% .81 2000
2 12% 24% 11% .46 800
3 20% 12% 4% .66 600
4 0% 0% 90% 13.16 30
Man Even has determined that they will need to mix three distinct feeds to meet the nurturional needs of the horses they are boarding this month. FEED A will need a minimum of 24% protein in the blend, a minimum of 14% fat, and a minimum of 9% vitamin C. They will need to mix 1400 lbs. of Feed A. FEED B will need a minimum of 20% protein, a maximum of 9% fat, and a minimum of 12% vitamin C. They will need to have 600 lbs. of Feed B. FEED C will need a minimum of 15% protein, a minimum of 13% fat, and a minimum of 6% vitamin C. They expect to need 1000 lbs of Feed C.
Construct a linear program to determine most cost efficient blend of the four input mixers. Must have variable defintions, objective function and constraints in the linear program.