A fraternity house spends a total of $100 per month to purchase three different kinds of beer. A, B, and C, which cost $16, $24, and $32 per case, respectively. Let nA, nB, and nC, be the number of cases of each type of beer purchased each month. The $100 monthly expenditure impses a restriction on the allowed values of the parameters (nA, nB, nc) a) Write down an "equation of state" that describes this system i. e. a single equation involving nA, nB, and nC that correctly expresses the above restriction.
b) Draw teh equatin of state as a surface in the three-dimensional space (nA, nB, nC)
c) Derive an expression for one of the parameters as a function of the other two (e. g. nC-f(nA, nB)) derive a similar expression for the remaining two parameters. In each case, which are independent and which are dependent variables.