Engineers at Waterworks Ltd. have designed a pipeline that provides a throughput of 100,000 gallons of water per 24-hour period that is to supply residents in a small town. By increasing the diameter of the pipeline by 1 inch, the throughput of water would increase by 5,000 gallons per day. Alternatively, throughput could be increased by 7,000 gallons per day using the original pipe diameter with pumps that had 100 more horsepower. a. Estimate the marginal rate of technical substitution between pump horsepower and pipe diameter. b. Assuming the cost of additional pump size is $7 per horsepower and the cost of larger diameter pipe is $250,000 per inch, does the original design exhibit the property required for optimal input combinations? Why or why not?