Final answer:
The question involves maximizing Sam's utility function U(C,T)=10C+6T subject to the budget constraint 4C+3T=24. This can be accomplished by substituting T from the budget constraint into the utility function and finding the value of C that maximizes utility, then calculating T accordingly. This optimization problem is common in microeconomics and requires an understanding of utility maximization and budget constraints.
Step-by-step explanation:
The student's question is about finding the optimal combination of coffee and tea that Sam will consume given his utility function U(C,T)=10C+6T, and his budget constraint 4C+3T=24. To solve this, we need to maximize Sam's utility subject to his budget constraint. The utility maximization problem is a cornerstone concept in microeconomics and can be solved using the method of Lagrange multipliers or by setting up the equation of the line representing the budget constraint and equating the marginal utilities per dollar spent on coffee and tea.
In this specific case, since we don't have a restriction on Sam preferring more of one good to another, and the utilities for each are constant, we can simply find the maximum of the function by setting the total derivatives equal to zero, and then substituting into the budget constraint.
However, we can also use another approach by substituting T from the constraint into the utility function, deriving it with respect to C, setting the derivative to zero to find the maximum utility point, and then substituting back to find the optimal quantities of C and T. So, the general procedure for solving this kind of problem is understanding how to maximize utility given the budget constraint.