Three desk shelves-I, II, and III-are being stocked with seven types of food. Bread, Biscuits, Pizzas, Shakes, Cake, Sweet, and Sandwich are to be placed in the shelves so that the goods belonging to any given type are all together in one shelf and no shelf contains more than three types of food. The arrangement of the types of food is subject to the following further constraints: Bread and Cake must be in a shelf together. Neither Biscuits nor Shakes can be in the same shelf as Pizzas. Neither Biscuits nor Shakes can be in the same shelf as Sweet. The Sweet must be in either shelf I or shelf II. Each type of goods must be in some shelf or other. If Cake is in II, which of the following is acceptable?

Explanation: Foods: Bread (B), Biscuits (Bi), Pizzas (P), Shakes (Sh), Cake (C), Sweet (Sw), Sandwich (Sa). Max 3 foods per shelf. Rules: (1) B & C together. (2) Bi, Sh \(\neq\) P. (3) Bi, Sh \(\neq\) Sw. (4) Sw is in I or II. (5) All foods used. Given: **Cake (C) is in Shelf II**. Rule (1) \(\implies\) Bread (B) must also be in Shelf II. Shelf II = {B, C}. Max 3 foods/shelf. Remaining foods: {Bi, P, Sh, Sw, Sa}. Remaining shelves: I, III. Rule (4) \(\implies\) Sweet (Sw) is in I or II. Since Sw \(\neq\) II ({B, C} is in II and max is 3), Sw must be in **Shelf I**. Shelf I = {Sw}. Rule (3) \(\implies\) Bi, Sh \(\neq\) Sw. Since Sw is in I, Bi and Sh \(\neq\) I. Bi and Sh must be in **Shelf III**. Shelf III = {Bi, Sh}. Remaining food: {P, Sa}. Remaining shelves: I, II. Shelf I max is 3, currently has {Sw}. Shelf II max is 3, currently has {B, C}. Rule (2) \(\implies\) Bi, Sh \(\neq\) P. Bi and Sh are in III. P must be in I or II. P \(\neq\) III. P can be in I or II. Case A: P in I. Shelf I = {Sw, P}. Sa must be in II. Shelf II = {B, C, Sa}. Shelf I: {Sw, P}, Shelf II: {B, C, Sa}, Shelf III: {Bi, Sh}. All rules satisfied. This acceptable arrangement has **Sweets in I and Pizzas in I**. Option 5: **Sweets are in I and Pizzas are in II**. Check Option 5: Shelf I: {Sw}, Shelf II: {B, C, P}, Shelf III: {Bi, Sh, Sa}. This violates max 3 for Shelf II unless Sa is in III. Case B: P in II. Shelf II = {B, C, P}. Sa must be in I. Shelf I = {Sw, Sa}. Shelf I: {Sw, Sa}, Shelf II: {B, C, P}, Shelf III: {Bi, Sh}. All rules satisfied. This acceptable arrangement has **Sweets in I and Pizzas in II**. Thus, Option 5 is acceptable.