Question

Question 2. A doctor prescribes a sick freshman fruits (Banana and Orange) that provide Vitamin A, Vitamin B and Vitamin C. A pound of Banana contributes 8 grams of Vitamin A and 6 grams of Vitamin B and 2 grams of Vitamin C while a pound of Orange contributes 2 grams of Vitamin A and 6 grams of Vitamin B. A pound of Banana costs $4 and a pound of Orange costs $6. The student has to meet a minimum requirement of 27 grams of Vitamin A, 38 grams of Vitamin B and 6 grams of Vitamin C. The student should avoid taking more than 53 grams of Vitamin A and 71 grams of Vitamin B to avoid side effects such as nausea and vomiting. The pounds of banana eaten should be more than the pounds of orange eaten by at least 2 pound. Formulate a linear programming problem to help the poor freshman to choose the fruit mix to recover fast

Answer 1

Formulation of Linear Programming Problem:

	Vitamin A (gm/pound)	Vitamin B (gm/pound)	Vitamin c (gm/pound)	Cost ($/pound)
Banana (X1)	8	6	2	4
Orange (X2)	2	6	0	6
Minimum Requirement	27	38	6
Maximum Requirement	53	71	-

So, we need to minimize the total cost of purchasing:

MINIMIZE Z = 4 X₁ + 6 X₂

Subject to Constraints:

• 8 X₁+ 2 X₂ >= 27
• 6 X₁+ 6 X₂ >= 38
• 2 X₁+ 0 X₂ >= 6
• 8 X₁+ 2 X₂ <= 53
• 6 X₁+ 6 X₂ <= 71
• X₁ > 0 , X₂> 0