Answer:
Therefore, Olivia should buy 10 apples and 8 bananas to maximize her utility.
Explanation:
Let A represent the number of apples bought and B represent the number of bananas bought. Therefore since Olivia has $4 to spend:
0.2A + 0.25B = 4 (1)
Also, the tangency condition can be used to find the optimal amount of A to relative to B. It is give as:
[tex]MU_A/P_A=MU_B/P_B\\\\\frac{3\sqrt{\frac{B}{A} } }{0.2}= \frac{3\sqrt{\frac{A}{B} } }{0.25}\\\\15\sqrt{\frac{B}{A} }=12\sqrt{\frac{A}{B} }\\\\squaring\ both\ sides:\\\\\frac{225B}{A} =\frac{144A}{B}\\\\225B^2=144A^2\\\\B^2=0.64A^2\\\\Taking\ square\ root:\\\\B=0.8A[/tex]
Put B = 0.8A in equation 1:
0.2A + 0.25(0.8A) = 4
0.2A + 0.2A = 4
0.4A = 4
A = 10
B = 0.8(A) = 0.8(10) = 8
Therefore, Olivia should buy 10 apples and 8 bananas to maximize her utility.
