The City of Imperial Falls contracts with Evergreen Waste Collection to provide solid waste collection to households and businesses. Until recently, Evergreen had an exclusive franchise to provide this service in Imperial Falls, which meant that other waste collection firms could not operate legally in the city. The price per pound of waste collected was regulated at $25$ percent above the average total cost of collection.

Cost data for the most recent year of operations for Evergreen are as follows.

Administrative cost $ $409,000$

Operating costs$$trucks $1,325,000$

Other collection costs $329,000$

Data on customers for the most recent year are as follows.

Households Businesses

Number of customers $12,9004,800$

Waste collected $($tons$)4,90013,800$

The City Council of Imperial Falls is considering allowing other private waste haulers to collect waste from businesses, but not from households. Service to businesses from other waste collection firms would not be subject to price regulation. Based on information from neighboring cities, the price that other private waste collection firms will charge is estimated to be $$0\mathrm{.}05$ per pound $(=$ $$100$ per ton$).(1$ ton $=2,000$ pounds$)$

Evergreen's CEO has approached the city council with a proposal to change the way costs are allocated to households and businesses, which will result in different rates for households and businesses. She proposes that administrative costs and truck operating costs be allocated based on the number of customers and the other collection costs be allocated based on pounds collected. The total costs allocated to households would then be divided by the estimated number of pounds collected from households to determine the cost of collection. The rate would then be $25$ percent above the cost. The rate for businesses would be determined using the same calculation.

Required:

a$.$ Based on cost data from the most recent year, what is the price per pound charged by Evergreen for waste collection under the current system $($the same rate for both types of customers$)?$

b$.$ Based on cost and waste data from the most recent year, what would be the price per pound charged to households and to businesses by Evergreen for waste collection if the CEO$$s proposal were accepted?