Please can you help me with this past paper question. Please could you give detail and reference to theory that you use to solve it. It will be rewarded by a excellent review!

Consider the utility function of a consumer who obtains utility from consuming only two goods, 1 and 2 , in fixed proportions. Specifically, the utility of the consumer requires the consumption of two units of 2 for each unit of 1.

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.