Question

Your automobile assembly plant has a Cobb-Douglas production function given by q =100x^(0.3)+y^(0.7), where q is the number of automobiles per year, x is the number of employees, and y is the monthly assembly line budget (in thousands of $). Annual operating costs amount to an average of $60 thousand per employee plus the operating budget of $12y thousand (I don't know if the y is a typo and it just means $12,000). Your annual budget is $1,200,000. Find the number of employees you should hire, what should your assembly line budget be to maximize productivity, and find max productivity.

Answer 1

I'm not asking for an answer but help understanding and setting this up. So far I get that q= # cars/year, x = # employees, y = monthly budget in $. The Annual costs are $60,000 per employee + $12,000 in operations. The company's total budget is $1,200,000 per year. The first step would be to set the constraints and I know those would come from the costs, but I'm not sure how to set those up. I'm supposed to use Substitution or Lagrange multiplier methods. This is a Calculus question and it will require the use of partial derivatives.