Final answer:
Kate would consume approximately 4 units of good x if she chooses the bundle that maximizes her utility subject to her budget constraint.
Step-by-step explanation:
To find the utility-maximizing choice, we need to find the bundle that maximizes Kate's utility while staying within her budget constraint. Kate's utility function is U(x,y)=4√x+y, and the prices of goods x and y are $1 and $2 respectively. Kate's income is $100.
Let's assume Kate consumes 'x' units of good x and 'y' units of good y. According to her budget constraint, the total amount she can spend is $100, which can be expressed as 1x + 2y = 100.
We can substitute the value of y from the budget constraint equation into the utility function to get U(x) = 4√x+(100-2x)/2. Differentiate U(x) with respect to x, set the derivative equal to 0, and solve for x. The solution will give us the number of units of good x that Kate would consume to maximize her utility.
By solving this equation, we find that Kate would consume approximately 4 units of good x (Choice c) if she chooses the bundle that maximizes her utility within her budget constraint. Therefore, the answer is option c: 4 units of good x.