Question

The company that produces a table lamp has two production lines, A and B in its factory.
Suppose that the cost of producing x units of the table lamp in the production line A is (3x + 8)x dollars. The cost of producing y units of the same table lamp in the production line B is (2y + 6)y dollars. Now, the company has an order for 200 units of table lamp and plans to operate the both production lines.
Note that this is a constrained optimization problem. Use the Lagrangian method.

i) How many table lamps should the company produce in production lines to satisfy this order and minimize its cost of production?
ii) Using the bordered Hessian, confirm that your answer in part i) is a minimum.
iii) Explain the economic meaning of x

Answer 1