Final Answer:
The cost function is C(x₁, x₂) = 6x₁ + 3x₂.
Step-by-step explanation:
The production function f(x₁, x₂) = min(x₁/2, 3x₂) implies that the output is the minimum of x₁/2 and 3x₂. To find the cost function, we need to multiply the cost of each input by the amount used in production. Given that the cost of input 1 is 6 and input 2 is 3, the cost function C(x₁, x₂) can be expressed as C(x₁, x₂) = 6x₁ + 3x₂. This is because for every unit of input 1 used in production, the cost is 6 times that amount, and for every unit of input 2 used, the cost is 3 times that amount.
To illustrate this with an example, if the production requires using 4 units of input 1 and 2 units of input 2, the total cost would be C(4, 2) = (6 4) + (3 2) = 24 + 6 = 30.
In summary, the cost function C(x₁, x₂) = 6x₁ + 3x₂ represents the total cost of production based on the quantities of inputs used.