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Expert: - 4/24/2009


Question
A company find that it can operate in either of two modes:
1. Fixed Costs of $100,000/yr with variable costs of $200/unit
2. Fixed costs of $200,000/yr with variable costs of $100/unit
At what level of output would the firm make the same profit using either mode above?  The firm is paying no taxes.

Answer
Since all of the variables are in $, per year, and units,
I won't put in the notation, but just the numbers.
I'll bring back up the units at the end of the problem.

The equations are 1. 100,000 + 200x and 2. 200,000 + 100x.

They are equal when ...

Well, let's set them equal and see.

100,000 + 200x = 200,000 + 100x =>
200x - 100x = 200,000 - 100,000 =>
100x = 100,000.

From this equation, it can be seen that x = 1000 units
makes these two equation interchangable.
If the production is at this level, either method costs $300,000.

It wasn't asked for, but ...
If there are more than 1000 units made, choose 2.
If there are less than 1000 units made, choose 1.

The answer was really given a while ago at x = 1000 units.

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Scott A Wilson

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I can answer any question in general math, arithetic, discret math, algebra, box problems, geometry, filling a tank with water, trigonometry, pre-calculus, linear algebra, complex mathematics, probability, statistics, and most of anything else that relates to math. I can even tell you it takes me over 2,000 steps to go a mile, but is that relevant?

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Experience in the area; I have tutored people in the above areas of mathematics for almost two years in AllExperts.com. I have tutored people here and there in mathematics since before I received a BS degree almost 25 years ago. In just two more years, I received an MS degree as well, but more on that later. I tutored at OSU in the math center for all six years I was there. Most students offering assistance were juniors, seniors, or graduate students. I was allowed to tutor as a freshman. I tutored at Mathnasium for well over a year. I worked at The Boeing Company for over 5 years. I received an MS degreee in Mathematics from Oregon State Univeristy. The classes I took were over 100 hours of upper division credits in mathematical courses such as calculus, statistics, probabilty, linear algrebra, powers, linear regression, matrices, and more. I graduated with honors in both my BS and MS degrees. Past/Present Clients: College Students at Oregon State University, various math people since college, over 7,500 people on the PC from the US and rest the world.

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My master's paper was published in the OSU journal. The subject of it was Numerical Analysis used in shock waves and rarefaction fans. It dealt with discontinuities that arose over time. They were solved using the Leap Frog method. That method was used and improvements of it were shown. The improvements were by Enquist-Osher, Godunov, and Lax-Wendroff.

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Master of Science at OSU with high honors in mathematics. Bachelor of Science at OSU with high honors in mathematical sciences. This degree involved mathematics, statistics, and computer science. I also took sophmore level physics and chemistry while I was attending college. On the side I took raquetball, but that's still not relevant.

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I earned high honors in both my BS degree and MS degree from Oregon State. I was in near the top in most of my classes. In several classes in mathematics, I was first. In a class of over 100 students, I was always one of the first ones to complete the test. I graduated with well over 50 credits in upper division mathematics.

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My clients have been students at OSU, people nearby, friends with math questions, and several people every day on the PC, and you're probably make one more.

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