Question

A company manufactures a product that requires three raw materials x, y, z which are purchased at $12, $20, and $50 per unit of raw material respectively. Taking into consideration all manufacturing costs, the company has devised a productivity function P(x, y, z) = 100 x ^(1/4) y ^(1/2 )z^( 3/4) . (i) Given a budget of $36000, use the Lagrange multiplier technique to compute the optimum quantity of raw materials to maximise productivity. If the session to which you submit your assignment differs from the one you physically attend, fill in the cover sheet appropriately. (ii) Compute the value of the Lagrange multiplier λ at the critical values of x, y, z. Interpret what this value means; e.g. if the budget is increased by $1, what does the value of λ say about the expected change in productivity

Answer 1