Hammoud is planning to start a diet program. Following are the main ingredients of his diet: milk, bread, rice, eggs, vegetables, chicloen, lamb, fish, halawa, and ice-cream. The related information of the ingredients are given as follows: Following are the main restriction of his diet plan for a given meal: (i) The total calories intake per meal should be 80050. (ii) The total protein intake per meal should be 6010. (iii) The total fiber intuke per meal should be 155. (iv) He cannot eat more than three types of main ingredients in a meal. (v) If milk is taken in the meal, then bread and egs mist be part of the meal. (vi) If lamb or chicken is taken in the meal, then fish should not be taken in that meal. (vii) If bread and eggs are part of the meal, then milk must be part of that meal. (viii) Either halawa is included or ice-cream is included in the meal (but not both). (ix) Chicken, lamb and fish cannot be in ore meal. (x) No main ingredient must be taken more than two time in a day. Now, answer the following: (a) Define a variable that captures the sumber of units of the main ingrestients. (b) Using the above variable, build the constraints corresponding to restriction (i), (ii) \& (iii). (c) Can you use the above sariahle to build the rest of the restrictions? If not, then define a new variable and relate it to the previons variable. (d) Using the new or old variable, build the rest of the constraints. (e) If the goal is find a meal with lowest total cost, thes define the corresponding objective function. (f) Write the complete mathematical formulationt with the following modifications: - The diet plan is for a mouth ( 30 days), where each day should contain (3) meals. - The goal is to reduce the total cost for one month diet plan. - Restriction (i) to (viii) are applicable for each meal - A main ingredient should not be incluted in all the three meal of a day. - Every main ingredient should be taken at-lesst ouce per 5 days. co Note: You may need to apdate the nariable defunitions and define parumeters, in-order to rewerite the entine model. 'Note: In Part (f), write an implicit model, that is, use sammation () and enumerution (V) symbols wherever possible. For summation symbol, specify the limits of the sammation. If you use enumeration symbol, make sure the index range is clearly defined in your solution