MASSACHUSETTS INSTITUTE OF TECHNOLOGY

Thermodynamics of Materials

3.00 Fall 2001

W. Craig Carter

Department of Materials Science and Engineering

Massachusetts Institute of Technology

77 Massachusetts Ave.

Cambridge, MA 02139

Problem Set 1: Due Fri. Sept. 14, Before 5PM in 4-047

Exercise 1.1

Bad News

Your plans next summer to catch a lucrative job at a dotcom have been mercilessly dashed by ``irrational exuberance.''

Good News

You have found a lucrative job nearby anyway!

Bad News

Your job is to sell fruits and vegetables for the International House of Tutti Frutti Panoply Conglomerate to the mollycoddled students at Harbored University.

Good News

The students at Harbored pay with twenty dollar bills fresh from the ATM and either don't bother or can't count their change!

Bad News

The avaricious bureaucratic muddlers at Harbored levy a weekly tax based on your average supply of fruits and vegetables--and you don't have time to make a daily inventory.

More Bad News

The sorcerer's apprentices of IHTFP conglomerate send you apples at a constant rate of $\dot{A}$, bananas at rate $\dot{B}$ and carrots at rate $\dot{C}$.

Construct a model for the value of your inventory. You may need to introduce symbols for processes that affect your inventory, such as $\dot{R}_A$, $\dot{R}_B$, $\dot{R}_C$ for the rate of purchases of apples, bananas and carrots. Carefully consider all the various processes that would affect your inventory. Is it reasonable that your average inventory is a function of only $\dot{A}$, $\dot{B}$, $\dot{C}$, $\dot{R}_A$, $\dot{R}_B$, and $\dot{R}_C$?