Optimal Input Mix. Third World Solutions, Inc., has designed a manual water pump that attains a flow rate of 5 gallons per minute using 1 manpower. If the diameter of the pump were increased by 1 inch, throughput would increase 4 gallons per minute. Alternatively, throughput could be increased by an additional 8 gallons per minute using the original pump diameter with one hydraulic chamber.
A. Estimate the marginal rate of technical substitution between hydraulic chambers and pump diameter.
B. Assuming the cost of additional hydraulic chamber size is $5 per chamber and the cost of a larger pump diameter is $2.50 per inch, does the original design exhibit the property required for optimal input combinations? If so, why? If not, why not?

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The Answer of Optimal Input Mix. Third World Solutions, Inc., has designed a manual water pump that attains a flow rate of 5 gallons per minute using 1 manpower. If the diameter of the pump were increased by 1 inch, throughput would increase 4 gallons per minute. Alternatively, throughput could be increased by an additional 8 gallons per minute using the original pump diameter with one hydraulic chamber.
A. Estimate the marginal rate of technical substitution between hydraulic chambers and pump diameter.
B. Assuming the cost of additional hydraulic chamber size is $5 per chamber and the cost of a larger pump diameter is $2.50 per inch, does the original design exhibit the property required for optimal input combinations? If so, why? If not, why not?