Please answer all questions step by step in detailed procedures.

L The Kingston City Council decided to open a new recycling plant to help divert more garbage away from the local landll. The new recycling plant, which is very similar to other recycling plants in the municipality of Kingston, will open next month. It will have 3 garbage separation systems, each costing $2,0Dl] per month to operate. It will also require some workers, who get a pay rate of $25 per hour. Each worker works for 14H hours per month [part-time workers cannot he hired}. The City of Kingston hired you as a consultant to help them start up the recycling plant. The city provides you with detailed production data of a very similar recycling plant, which includes the total amount of garbage processed (diluted :3; measured in kilogram (kg) per month], and the number of garbage separation systems {K} and total working hours (L) used in each month. a} Use the production data {available on the course website] to estimate the production mction for the new recycling plant. Assume the production can be best described by a Cobb-Douglas production function. Include the regression results 'om Excel in your assignment. (Note: For all estimated coefficients carry 4 nonzero digits to the right of the decimal point.) (4 paints} b} Right after its opening next month the recycling plant is expected to process 60,000 kg of garbage each month. l[liven the 3 garbage separation systems, how many workers should the city hire to ensure that all the garbage can be processed? What is then the total cost per month for the city? [4 points) c} You are not entirely sure whether it is really optiroal to use 3 garbage separation systems to process the , kg of garbage every month. Find the optimal number of garbage separation systems and workers that would minimize the total cost of processing l kg of garbage each month. How much would the city save compared to your answer from part (b)? (Hint: If the optimal number of garbage separation systems does not turn out to be a whole number, thll you need to check whether using the lower or the higher whole number of garbage separation systI-c is optimal (e.g., if you nd that H = 12.4, you need to consider H = 12 and K = 13]. Then nd the corresponding number of workers, and identify the optimal number of garbage separation systems based on a cost comparison.) [It] points}