The dietitian at a camp is planning breakfast for the first day of camp. The die
ID: 468015 • Letter: T
Question
The dietitian at a camp is planning breakfast for the first day of camp. The dietitian has the responsibility of providing a menu that satisfies the minimum nutrient requirements at the lowest cost. Two types of foods are being considered for the breakfast: toast and sausage.A piece of toast contains 2 milligrams of vitamin A, 3 milligrams of vitamin B, and 2 milligram of iron. A sausage contains 4 milligrams of vitamin A, 1.5 milligrams of vitamin B, and 2 milligram of iron. The minimum breakfast requirements of these nutrient elements are estimated to be:
16
The American Medical Association has published an article which reported that having more than four sausages for breakfast is not recommended for young people. The dietitian considers this one of the most important constraints. The unit costs of the food are: toast, 4 cents; sausage, 8 cents. Formulate this problem as a linear programming problem , solve it by the software and answer the following question:
How many toasts should be given in the breakfast?
Nutrient Requirement (mg) Vitamin A 20 Vitamin B 15 Iron16
Explanation / Answer
Let us assume decision variables-
Toasts (number of units) = x1
Sausage (number of units) = x2
Cost per units in cents –
X1 = 4 cents /unit; x2 = 8 cents /unit
Obj. Function : Minimize the total cost : 4x1 + 8x2
Constraints:
Vit A >= 20 mg
Vit B >= 15 mg
Iron >16 mg
Solution using solver shown below:
Qunatity :
Number of toasts ; 4
Number of sausage : 4
Total Cost: 48 cents
Toast sausage Cost in cents /unit 4 8 Toast sausage Vitamin A 2 4 Vitamin B 3 1.5 Iron 2 2 CC Dec. Var 4 4 Constraints Vit A 24 >= 20 Vit B 18 >= 15 Iron 16 >= 16 Sausage 4 <= 4 Obj.Function in cents 48