A mop company can produce mops using x units of capital and y units of labor, with production costs dollars. With a budget of $400,000, the maximum production is 65,000, using $300,000 in capital and $100,000 in labor. The Lagrange multiplier is . What are the units for ?
A)Number of budget dollars per mop
B)Number of mops per budget dollar
C)Number of units of capital per mop
D)Number of units of labor per budget dollar

Question

A mop company can produce  mops using x units of capital and y units of labor, with production costs  dollars. With a budget of $400,000, the maximum production is 65,000, using $300,000 in capital and $100,000 in labor. The Lagrange multiplier is  . What are the units for  ?
A)Number of budget dollars per mop 
B)Number of mops per budget dollar 
C)Number of units of capital per mop 
D)Number of units of labor per budget dollar

Quizplus · Accepted Answer

The Lagrange multiplier represents the rate of change of production costs with respect to the budget. In other words, it tells us how much the cost of producing one additional mop will increase if we increase the budget by one dollar. Therefore, the units for the Lagrange multiplier are "number of mops per budget dollar."

A Mop Company Can Produce Mops Using X Units