Math and Science Solutions for Businesses/Econ/microeconomics


A firm produces two goods. For production of good1 they use raw material1 and one machine. For production of good2 they use raw material2 and the same machine.

The costs for using the machine is v^2$/day where v is the amount of used machine hours per day. To produce one unit of good1 do they have to use 1 hour of machine time. And to produce one unit of good2 they have to use 2 hours machine time. The firm produces atm. 4 units per day of each.

a) What is the total machine cost and the special machine costs for each good.

I'm not sure I quite understand the question as it seems that more information is needed (I'm also not sure what "atm." means):

- how many hours a day can the machine be run?
- how many units of good1 and 2 are desired?

For an optimization problem, you need to specify the cost of the materials and the value of the produced goods. Please send a follow-up with more explanation.

Math and Science Solutions for Businesses

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Randy Patton


Questions regarding application of mathematical techniques and knowledge of physics and engineering principles to product and services design, optimization, prediction, feasibility and implementation. Examples include sales and product performance projections based on math/physics models in addition to standard regression; practical and cost effective sensor design and component configuration; optimal resource allocation using common tools (eg., MS Office); advanced data analysis techniques and implementation; simulation and "what if" analysis; and innovative applications of remote sensing.


26 years as professional physical scientist and project manager for elite research company providing academic quality basic and applied research for government and defense industry clients (currently retired). Projects I have been involved in include: - Notional sensor performance predictions for detecting underwater phenomena - Designing and testing guidance algorithms for multi-component system - Statistical analysis of ship tracking data and development of anomaly detector - Deployed vibration sensors in Arctic ice floes; analysis of data - Developed and tested ocean optical instrument to measure particles - Field testing of protoype sonar system - Analysis of synthetic aperture radar system data for ocean surface measurements - Redesigned dust shelters for greeters at Burning Man Festival Project management with responsibility for allocation and monitoriing of staff and equipment resources.

“A Numerical Model for Low-Frequency Equatorial Dynamics” (with Mark A. Cane), J. of Phys. Oceanogr., 14, No. 12, pp. 18531863, December 1984.

MIT, MS Physical Oceanography, 1981 UC Berkeley, BS Applied Math, 1976

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