A Diet Problem Example

Animal feed is produced by mixing four ingredients: corn, soybeans, oats and fishmeal. The nutritional and cost data is given as follows (nutrients are specified per pound of ingredient):
 
Nutrient
Corn
Soybeans
Oats
Fishmeal
 Daily requirement
Protein (g)
10
9
11
8
 Minimum of 40 g.
Calcium (mg)
50
45
58
50
 Minimum of 120 mg.
Fat (g)
30
90
10
5
 Minimum of 20 g. 
Maximum of 100 g.
Calories
900
1200
1000
600
 Minimum of 4500 cal.
Cost ($/lb.)
.60
.30
.35
.85
  

(a) Formulate an LP model to satisfy the daily requirements at minimum cost.

(b) Formulate the problem in Excel, and find the optimum solution with Solver.