make sure to PARAMETERIZE the LP. There shouldn't be any numbers in the answer

All the numbers given are just examples.

4. You have been put in charge of procuring ingredients for tonight's soire. Specifically, to finishing cooking the meal, you need 20lbs of carrots, 15 lbs of broccoli, and 30 lbs of cauliflower. Regrettably, your store only sells mixtures of these products. Each mixture is described in Table 3 below. Mixture 1 Mixture 2 Mixture 3 Table 1: Information per lb of vegetable mixture Carrots (lbs) Broccoli (lbs) Cauliflower (lbs) Price per lb lbs Available 0 0.5 0.5 $5 20 0.4 0.3 0.3 $2 30 0.4 0.2 0.4 $4 40 For example, if you buy 5 lbs of mixture 2, then you obtain 5.0.4 2lbs of carrots, 5.0.3 = 1.5lbs of broccoli, and 5.0.3 = 1.5lbs of cauliflower for a total cost of 5- $2 = $10. Any extra ingredients can be resold in the market the following day. Specifically, extra carrots, broccoli, and cauliflower purchased can be sold for $1, $1.5, and $1.25 per pound respectively. (a) Formulate an LP to help determine the optimal shopping list that minimizes cost. Your answer should be parameterized to handle any number/set of mixtures and ingredients. Clearly label each part of your answer. (b) You recently learned of an premium delivery service that can directly provide you individual amounts of each ingredient. You can purchase carrots, broccoli, and and cauliflower directly for $4, $5, and $6 per lb respectively. Update your model to in- clude this additional purchasing option. Your answer should be still be parameterized for any number of mixtures/ingredients. You only need to write new/edited variables, constraints, and/or objective function