Answer Happy

1. "Coffee House" Equation of State (4 pts) A coffee house spends a total of $100 per month to purchase three different kinds of coffee, A, B, and C, which cost $5, $10, and $15 per pound, respectively. Let na, nb, and nc be the number of pounds of each type of coffee purchased each month. The $100 monthly expenditure imposes a restriction on the allowed values of the parameters (na, Ne, nc). (a) Write down an "equation of state" that describes this system, i.e. a single equation involving na, ng, and ne that correctly expresses the above restriction. (b) Draw the equation of state as a surface in the three-dimensional space (na, N3, 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 one of the remaining two parameters (e.g. np = g(na, nc)). In each case, which are the independent, and which the dependent variables?