Final answer:
With an income of $8 and the price of x at $1, Matt will purchase the maximum possible units of x within his budget, which is 8 units. The options provided do not include the correct answer.
Step-by-step explanation:
The student's question revolves around finding out how many units of good x Matt would demand, given his utility function, which is the minimum of (f(x), 4y+5z), the prices of the goods, and his income. With Matt's income being $8, and considering the prices of goods x, y, and z to be $1, $4, and $7 respectively, Matt would want to maximize his utility within his budget constraint. Since we don't have the explicit form of f(x), we cannot calculate the exact utility from x. However, we can note that with a budget of $8, Matt cannot purchase more than 8 units of x (because the price of x is $1). Furthermore, any amount spent on y or z would reduce the amount available to spend on x. Since y and z are more expensive and we want to find the maximum demand for x, we will allocate all of the budget towards buying x, assuming that x gives positive utility. Therefore, with an income of $8 and the price of x being $1, Matt will demand 8 units of x, so none of the given options (a) 1, (b) 2, (c) 3, or (d) 4 are correct.