Question

Your automobile assembly plant has a Cobb-Douglas production function given by

q = 100x^0.3y^0.7,

where q is the number of automobiles it produces per year, x is the number of employees, and y is the monthly assembly-line budget (in thousands of dollars). Annual operating costs amount to an average of $60 thousand per employee plus the operating budget of $12y thousand. Your annual budget is $1,200,000. How many employees should you hire and what should your assembly-line budget be to maximize productivity? (Round your budget to the nearest thousand dollars.)

number of employees

assembly-line budget$ thousand

What is the productivity at these levels? HINT [See Example 5.] (Round your answer to the nearest automobile.)

automobiles per year

Answer 1