Question

A steel manufacturer can produce P (K,L) tons of steel using K units of capital and L units of labor, with production costs C(K, L) dollars. With a budget of $950,000, the maximum production is 10,000 tons, using $700,000 of capital and $250,000 of labor. The Lagrange multiplier is a = 0.14. (a) What is the objective function? YPCK,L) V (b) What is the constraint? TCK) 3 - (C) What are the units for 2? tons/dollar (d) What is the practical meaning of the statement i = 0.14? Every extra dollar of budget the extra dollar of budget increases maximal production by approximately 2 = 0.14 tons.

Answer 1

Clearly, P(K,L) is our objective function which needs to be maximized.

In simple words, a constraint function can be transformed into a different form that is equivalent to the original function. That is to say, that by performing some algebra on the constraint function we can change it to the actual objective funtion.

The constraint that is C(K,L) will be :

$(UR) K + $(UI) L = $950,000

where $(U_k)$ is unit cost of capital. And $(U_l)$ is the unit cost of labour. Hence, if we take in consideration the cost of K units of capital and L units of labour, the total cost should be less than the total budget of the steel company.

And since, in the question its already stated that the steel manufacturer has a fixed budget, therefore, we will be using the this as our constraint.