Exam sample 2

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Problem 2 To celebrate the amazing mark you will get in this Energy Modelling and Scenarios exam: you decide to go SweetSweetWay, a candy shop in Milan city centre. You can choose between three types of chocolates (C1, C2, C3), gummy candies (G1, G2, G3), and liquorice candies (L1, L2, L3). The pleasure you get from eating candies can be modelled as: 𝑈(𝒒) = ∑ 𝑞𝑖 𝑎𝑖 𝑖 Where 𝒒 is the vector of the 9 different candies you can buy. The list of candies, together with the price for 100 grams of candies and exponents 𝛼𝑖 can be found in the table below: Goods C1 C2 C3 G1 G2 G3 L1 L2 L3 Prices (€/100grams) 10 20 40 30 10 20 50 30 40 Alpha 0.05 0.15 0.1 0.05 0.25 0.1 0.05 0.15 0.1 Since you really NEED to celebrate this occasion, you decide to allocate 𝑅 = 10 € to buy candies. Your objective is to enjoy yourself as much as you can by choosing a specific mix of candies to eat, considering that you cannot spend more than your (admittedly pretty huge) budget. Now: 1. Write a GAMS programme to solve this question (frame it so that the answer you get will be in grams) 2. What will change if the price of all chocolates suddenly increases by 25%? Modify the code to account for this fact. 3. The alphas of all the candies but the liquorices increases by 0.05, modify the code to add this. 4. All candies are not charged by the weight, but by the quantity. The prices for the quantities (in €/piece) are equal to the prices for 100 grams divided by 1000. Change the code to account for this fact. The utility function changes too, and it becomes: 𝑈(𝒒) = ∑ 𝑞𝑖𝛼𝑖 𝑖