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Consider the utility function of a consumer who obtains utility from consuming only two goods, q1 and q2, in fixed proportions. Specifically, the utility of the consumer requires the consumption of two units of q2 for each unit of q1. i. Report the mathematical expression of the utility function of the consumer. ii. Provide a diagram of the corresponding indifference curves. iii. Provide at least one example and economic intuition. Suppose that the consumer has available income equal to Y, and the price of the goods is respectively pl and p2. i. Derive the expressions of the quantities that maximise the utility of the consumer under the budget constraint. ii. Provide a diagram of the optimal solution.