Question

1. Vitamins B1 and B2 are found in two foods F1 and F2. 1 unit of F1 contains 3 units of B1 and 4 units of B2. 1 unit of F2 contains 5 units of B1 and 3 units of B2 respectively. The minimum daily prescribed consumption of B1 & B2 is 50 and 60 units respectively. The cost per unit of F1 & F2 is Rs. 6 & Rs. 3 respectively. Formulate as LPP.

Answer 1

Let

x = number of units of F₁ to consume

y = number of units of F₂ to consume

Objective Function:

Minimize the cost of consumption, which can be expressed as:

Cost = 6x + 3y (since the cost per unit of F₁ is Rs. 6 and F₂ is Rs. 3

Constraints:

B₁ consumption constraint:

The daily prescribed consumption of B₁ should be at least 50 units.

Considering the composition of B₁ in F₁ and F₂, we have:

3x + 5y ≥ 50

B₂ consumption constraint:

The daily prescribed consumption of B₂ should be at least 60 units. Considering the composition of B₂ in F₁ and F₂, we have:

4x + 3y ≥ 60

Non-negativity constraint:

The number of units of F₁ and F₂ consumed cannot be negative, so we have:

x ≥ 0

y ≥ 0

The formulated LPP can be summarized as follows:

Minimize: Cost = 6x + 3y

Subject to:

3x + 5y ≥ 50

4x + 3y ≥ 60

x ≥ 0

y ≥ 0

By solving this LPP, we can determine the optimal values of x and y, which represent the number of units of F₁ and F₂ to consume in order to meet the minimum daily prescribed consumption of B₁ and B₂ while minimizing the cost of consumption.