The automobile assembly plant you manage has a Cobb-Douglas production function given by
P = 30x^0.5y^0.5
where P is the number of automobiles it produces per year, x is the number of employees, and y is the daily operating budget (in dollars). Assume that you maintain a constant work force of 130 workers and wish to increase production in order to meet a demand that is increasing by 80 automobiles per year. The current demand is 900 automobiles per year. How fast should your daily operating budget be increasing?

How do I solve this question?

Question

The automobile assembly plant you manage has a Cobb-Douglas production function given by
P = 30x^0.5y^0.5
where P is the number of automobiles it produces per year, x is the number of employees, and y is the daily operating budget (in dollars). Assume that you maintain a constant work force of 130 workers and wish to increase production in order to meet a demand that is increasing by 80 automobiles per year. The current demand is 900 automobiles per year. How fast should your daily operating budget be increasing?

How do I solve this question?

anonymous · Answer

Attached is a picture of my attempt at solving this problem. I'm not sure where I went wrong with it, any help would be appreciated.