Question

The problem is to determine the optimum daily production for three products that maximize the profits. Formulate the above production planning problem in L.P.P format.

Answer 1

Maximize 𝑍=2𝑥1+𝑥2+3𝑥3 Subject to: 3𝑥1+4𝑥2+3𝑥3≤43 5𝑥1+4𝑥3≤46 3𝑥1+6𝑥2+2𝑥3≤42 𝑥1,𝑥2,𝑥3≥0

Answer 2

The problem is formulated as an LPP by defining decision variables for the production of each product ($x_1, x_2, x_3$), an objective function to maximize total profit based on per-unit profit, and constraints representing the limited capacity of each operation, ensuring that the total resource consumption does not exceed the available capacity. Non-negativity constraints are also included as production quantities cannot be negative.