Your automobile assembly plant has a Cobb-Douglas production function given by
$q = x ^ { 0.5 } y ^ { 0.5 }$
Where q is the number of automobiles it produced per year, x is the number of employees, and y is the daily operating budget (in dollars). Annual operating costs amount to an average of $30,000 per employee plus the operating budget of $\$ 300 y$ . Assume you wish to produce 1,500 automobiles per year at a minimum cost. How many employees should you hire

A)180 employees
B) 75 employees
C) 30 employees
D) 150 employees
E) 225 employees

Question

Your automobile assembly plant has a Cobb-Douglas production function given by 
 $q = x ^ { 0.5 } y ^ { 0.5 }$  
Where q is the number of automobiles it produced per year, x is the number of employees, and y is the daily operating budget (in dollars). Annual operating costs amount to an average of $30,000 per employee plus the operating budget of $\$ 300 y$ . Assume you wish to produce 1,500 automobiles per year at a minimum cost. How many employees should you hire 
 
A)180 employees
B) 75 employees
C) 30 employees
D) 150 employees
E) 225 employees

Quizplus · Accepted Answer

To minimize costs, use the Cobb-Douglas production function and cost function. Set up the Lagrangian for cost minimization and solve for x and y. The optimal number of employees is 150.

Your Automobile Assembly Plant Has a Cobb-Douglas Production Function Given q=x0.5y0.5q = x ^ { 0.5 } y ^ { 0.5 }q=x0.5y0.5

Your Automobile Assembly Plant Has a Cobb-Douglas Production Function Given $q = x ^ { 0.5 } y ^ { 0.5 }$