from scipy.optimize import linprog

Coefficients of the objective function (minimize cost)

c = [1120, 1550, 1920]

Coefficients of the inequality (production constraint: at least 500 units per day)

A = [[-470.4, -384, -338.4]] # Negative for >= constraint

Right-hand side of the inequality

b = [-500] # Negative for >= constraint

Bounds for the variables (machine availability constraints)

x0_bounds = (0, 8) # Machine A x1_bounds = (0, 10) # Machine B x2_bounds = (0, 12) # Machine C

Solve the linear programming problem

result = linprog(c, A_ub=A, b_ub=b, bounds=[x0_bounds, x1_bounds, x2_bounds], method='highs')

resultThe optimal solution to minimize the production and quality control costs while producing at least 500 quality units per day is as follows:

• Use approximately 1.06 units of Machine A.
• 0 units of Machine B and 0 units of Machine C are required.

The minimum total cost is approximately ₹1190.48 per day.

This solution ensures that the company produces the required 500 quality units with the least possible cost, primarily using Machine A.

Would you like further details on how this solution was reached or how it can be interpreted in practice?

Five follow-up questions:

1. Would you like to know why Machines B and C are not used in the optimal solution?
2. Should we explore what happens if the required production is higher than 500 units?
3. How does the cost change if Machine A is unavailable for production?
4. Do you want to see how increasing defective costs affects the solution?
5. Should we check the impact of using additional machines in the model?

Tip:

If you're working on a larger problem with multiple constraints, using optimization software or libraries (like Python’s scipy.optimize or Excel Solver) can make the process much more efficient!