In the textile production problem, what is the objective function that minimizes production cost?

In the textile production problem, what is the objective function that minimizes production cost?

• A. Max Z = 9.50X1 + 3.50X2
• B. Min Z = 3.50X1 + 9.50X2
• C. Min Z = 9.50X1 + 3.50X2
• D. Min Z = 9.50X1 + 3.50X2 + 1

Answer: (C)

The total production cost is formed by multiplying how much you produce of each item by its cost per unit and adding those amounts together. Here, the cost per unit is 9.50 for X1 and 3.50 for X2, so the total cost is Z = 9.50X1 + 3.50X2. Since you want to minimize cost, you minimize this expression. A form that maximizes Z would push costs up rather than minimize them, and a form that swaps the coefficients would not reflect the actual costs. Adding a constant like +1 doesn’t change the optimal production mix, but it isn’t the proper way to state the objective. So the correct objective is Min Z = 9.50X1 + 3.50X2.

The total production cost is formed by multiplying how much you produce of each item by its cost per unit and adding those amounts together. Here, the cost per unit is 9.50 for X1 and 3.50 for X2, so the total cost is Z = 9.50X1 + 3.50X2. Since you want to minimize cost, you minimize this expression. A form that maximizes Z would push costs up rather than minimize them, and a form that swaps the coefficients would not reflect the actual costs. Adding a constant like +1 doesn’t change the optimal production mix, but it isn’t the proper way to state the objective. So the correct objective is Min Z = 9.50X1 + 3.50X2.