Please do all parts

Question 5. Ann is making a bowl of Laksa. In her Laksa she likes to have a bit of a range of proteins (chicken c, fish f, and tofu t), a good amount of green vegetables g; and a good amount of noodles n. These preferences can be represented by the utility a n 7 uc, fpt, 9, 1) = f / t* + g + n where ( 0 for each protein-type. a) For each of the following, determine whether Ann's preferences have this property. If they do, prove this. If not, provide a counter-example. i. Rational ii. Weakly Monotone iii. Strongly Monotone iv. Locally Non-satiated b) For each of the following, determine whether u satisfies this property. If it does, prove this. If not, prove it does not (either by providing a counterexample or otherwise) i. Homogeneous of degree 1 ii. Homothetic iii. Quasi-linear iv. Additively separable v. Weakly separable (Hint: u is weakly separable. You need to show this.] c) Suppose that Ann has decided to spend m dollars on the ingredients for her Laksa (she already has the soup). Using the maximisation process for weakly separable utility described in lectures, find the Marshallian demand for Laksa ingredients. d) Ann is given a coupon for 10% off either noodles or tofu. Should she use the coupon to buy noodles, or to buy tofu? Question 5. Ann is making a bowl of Laksa. In her Laksa she likes to have a bit of a range of proteins (chicken c, fish f, and tofu t), a good amount of green vegetables g; and a good amount of noodles n. These preferences can be represented by the utility a n 7 uc, fpt, 9, 1) = f / t* + g + n where ( 0 for each protein-type. a) For each of the following, determine whether Ann's preferences have this property. If they do, prove this. If not, provide a counter-example. i. Rational ii. Weakly Monotone iii. Strongly Monotone iv. Locally Non-satiated b) For each of the following, determine whether u satisfies this property. If it does, prove this. If not, prove it does not (either by providing a counterexample or otherwise) i. Homogeneous of degree 1 ii. Homothetic iii. Quasi-linear iv. Additively separable v. Weakly separable (Hint: u is weakly separable. You need to show this.] c) Suppose that Ann has decided to spend m dollars on the ingredients for her Laksa (she already has the soup). Using the maximisation process for weakly separable utility described in lectures, find the Marshallian demand for Laksa ingredients. d) Ann is given a coupon for 10% off either noodles or tofu. Should she use the coupon to buy noodles, or to buy tofu