Question

What combination of goods x1 and x2 should a firm produce to minimize cost if the cost function is c = x² ✕ y² and the firm has a production quota of 3b² + 4xy + 6y² = 140.

(b) how useful is this type of analysis?

Answer 1

To minimize cost, we need to find the values of x1 and x2 that satisfy the production quota while minimizing the cost function. The objective is to find the most efficient values for x1 and x2 that meet the production quota and minimize the cost function to maximize profits.

Step-by-step explanation:

To minimize cost, we need to find the values of x1 and x2 that satisfy the production quota while minimizing the cost function. Substituting the production quota into the cost function, we get c = (3b^2 + 4xy + 6y^2)^2. To minimize this function, we can take partial derivatives with respect to x and y and set them equal to zero. Solving these equations will give us the values of x1 and x2 that minimize cost.