please can you help me with the demand function and the optimal consumption please provide explanation

2. (25 points) Paris consumes only carrots (21) and sandwiches (2). Her utility function is: u(21, 12) = 5 Ina1 + 5 Inx2 (1) Suppose she has income m = 6 and faces prices p1 = 2 and p2 = 1. (a) (10) Calculate her optimal consumption bundle, (X1, 12) (Hint: It will save you time on part (b) if you first solve for the demand functions in general and then plug in specific values). (b) (5) Now suppose the prices change to p1 = 2 and p2 = 2. Calculate her optimal consumption bundle. (c) (10) Draw a graph that clearly marks the original and new consumption bundles, indifferent curves, and budget lines. Also, (approximately) indicate how to decompose this effect into income effect and substitution effect. (Note: you do not need to calculate the actual numbers in income effect and substitution effect. Just show approximate effect on graph.)