Please can you help me with this past paper from a micro exam. Can you also explain and give reference to any theories used. It would be rewarded with a great review!

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. 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.