The Automobile Assembly Plant You Manage Has a Cobb-Douglas Production $P = 10 x ^ { 0.3 } y ^ { 0.7 }$

Multiple Choice

The automobile assembly plant you manage has a Cobb-Douglas production function given by
$P = 10 x ^ { 0.3 } y ^ { 0.7 }$
Where P is the number of automobiles the plant produces per year, x is the number of employees, and y is the daily operating budget (in dollars) . You maintain a production level of 3,500 automobiles per year. If you currently employ 100 workers and are hiring new workers at a rate of 10 per year, how fast is your daily operating budget changing Round your answer to the nearest cent.

A) -$25.66 per year
B) $139.71 per year
C) -$2,566.04 per year
D) $25.66 per year
E) $17.96 per year