Optimal Input Mix

Essay

Optimal Input Mix. Boch, Ltd., has designed a fuel injector for oil fired generators that provides a throughput of 3 gallons of oil per minute. If the diameter of the industrial injector nozzle were increased by 1 centimeter, throughput would increase 1 gallon per minute. Alternatively, throughput could be increased by 2 gallons per minute using the original injector diameter with fuel pumps that had 50 more pounds of pressure (psi).
A. Estimate the marginal rate of technical substitution between pump psi and injector diameter.
B. Assuming the cost of additional fuel pump size is $10 per psi (due to changing of the pump and fuel supply peripheral), and the cost of larger diameter fuel injector is $400 per centimeter (due to machining of combustion units), does the original design exhibit the property required for optimal input combinations? If so, why? If not, why not?