JNU SIS 2019 Question 27: Demand theory and elasticity

Suppose $(x_1^*, x_2^*)$ maximizes utility subject to a budget constraint $p_1x_1 + p_2x_2 \leq y$, where $(p_1, p_2)$ is the price vector and $y$ is the income. Suppose the budget constraint holds as an equality at consumption bundle $(x_1^*, x_2^*)$, which yields utility $u^*$. Then, the consumption bundle that minimizes expenditure subject to attaining at least $u^*$ level of utility at price vector $(p_1, p_2)$