Humin Consulting Compnny (HCC) is planning to develop an app that can produce a diet plan based on the client's (or user's) preferences. The app will contain the following food categories and items: For examples Category-D contains items Coffec, Lemonade, Soda and Tea. Every food category brs its own number of items. Every item has its own serving unit, For example, Soda serving unit is is tin can, Lemonade serving unit is a bottle, Rlice serving unit is a bowl, etc. For each itean, hased on its serving unit, corresponding calories are calculated. The app should work as follows: Customer selects preferred itemy from the above table. Then the app suggests a meal plan that contains as many items preferred by the customer as possible. In addition to that, the meal plan will nbide by the following rales: R-(a): Both Fish and Milk cannot be included in a meal. R-(b): From Sodn, Tea, Coffee at most one item is included in a meal. R-(c): A meal should contain at least one item from Category-D. R(d) : Not less than (or equal) 2 items should be included from Category-G. R(e) : Not more than (or equal) 2 items should be included from Category-A. R(f) : At most two items from Category- C are inchuded in a meal. R(g) : Not all the items of Category-F can be included in A meal. R-(h): If none of Category-A is included, then all the items of Category-B must be included in a meal. R-(i): If more than 2 items from Category-F are included, then not more than one item from Category-E is included in a mesl. R(j) : If some of items from Category-C are included, then some items Category-A or Category-G (or both) should be included in a meal. R-(k): If all the items from Category-E are included, then all the items from Category-G and some items from Category- A are included in a meal. R-(1): A meal can have a minimum of 300 calories in total and maximum of 600 calories in total. If-(m): All the items from Category-A, C and E should liave only one serving in a meal (i.e., for example two chicken servings cannot be included in one meal). R(u):A meal cannot have more than 2 servings per item of Category-B. P(o) : A meal cannot have more than 3 servings per item of Category-D. R(P) : Every meal should contain at least 3 and at most 5 of the above 7 categories (A,B,C,D,E,F). Q1. Consider the following variables: Whe : : number of servings of item i from category c is included in the menl xi,n:={10ifitemifromcategorycisselectedinthemealotherwise where c={A,B,C,D,E,F,G} represents the available categorics, i=1,,4 corresponds to the items in each corresponding category. What are the types (restriction on domain) for the above variables. Q2. How many total variables are defined in Q1. Q3. Connect the variables: Write two if-then statements containing the above two variables based on logical reasoning. Hint: " fx1,e=0, then p ". Q4. Define a parameter that indicates number of calories per serving of an item. Q5. Define a parameter that captures the clients' item preferences. Q6. Write the explicit. mathematical model that produces a meal plan containing muximum number of items preferred by the client, while satisfying all the rules (R-(a) to R(p) ). - Note: The above questions are related. You can add new variables or pameters for the questions. Whenever a new parumeter is used, it must be clearly defined. Whenever a new variable is used, it must be clearly defined and connected. Write an explicit model in Q5. That is, do NOT use summation ()