Final answer:
Doreen would consume 30 units of good x if she chose the bundle that maximizes her utility subject to her budget constraint.
Step-by-step explanation:
To find the number of units of good x that Doreen would consume, we need to determine the bundle that maximizes her utility subject to her budget constraint.
Doreen's utility function is U(x,y) = 2x + 3y, where x represents the quantity of good x consumed and y represents the quantity of good y consumed.
The price of good x is $3, and the price of good y is $4. Doreen's income is $120.
We can set up the budget constraint equation as: Pxx + Pyy = I, where Px is the price of good x, Py is the price of good y, and I is Doreen's income.
Plugging in the values, we have: 3x + 4y = 120.
Now, we can maximize Doreen's utility function subject to the budget constraint.
Using the Lagrange multiplier technique, we set up the following equation:
2 = 3λ
3 = 4λ
3x + 4y = 120
Solving these equations, we find that x = 30 and y = 20.
Therefore, Doreen would consume 30 units of good x if she chose the bundle that maximizes her utility subject to her budget constraint.