Vitamins A and B are found in foods F₁ and F₂. One unit of food F₁ contains three units of vitamin A and four units of Vitamin B. One unit of food F₂ contains six units of vitamin A and three units of vitamin B. One unit of food F₁ and F₂ costs Rs.4 and Rs.5 respectively. The minimum daily requirement (for a person) of vitamins A and B is 80 units and 100 units respectively. Assuming that anything in excess of the daily minimum requirement of A and B is not harmful, formulate this problem as an LP problem to find out the optimum mixture of foods F₁ and F₂ at the minimum cost which meets the daily minimum requirement of vitamins A and B.
Answers
Answer:
Minimum Cost = 105
when 25F₁ & 1 F₂ is selected
Step-by-step explanation:
One unit of food F₁ contains three units of vitamin A and four units of Vitamin B.
F₁ = 3A + 4B
F₂ = 6A + 3B
Cost = 4F₁ + 5F₂
A ≥ 80
B ≥ 100
F₁ F₂ Vitamin A Vitamin B Cost
0 34 204 102 170
10 20 150 100 140
15 14 129 102 130
20 7 102 101 115
21 6 99 102 114
22 4 84 100 108
23 3 87 101 107
24 2 84 102 106
25 1 81 103 105
26 1 86 107 109
27 0 81 108 108
Minimum Cost = 105
when 25F₁ & 1 F₂ is selected