Question 7 A bakery makes two brands of cake, Butter cake and Cupcake. For a single batch of Butter cake, it requires 3kg of sugar and 2kg of butter, while for a single batch of Cupcake require 2kg of sugar and 4kg of butter. The bakery makes $3 profit on a batch of Butter cake and $4 profit on a batch of Cupcake. The bakery has access to at most 18kg of sugar and 20kg of butter per day. The store wants to determine the number of Butter cake and Cupcake to make in order to maximize profit. (a) Formulate a linear programming model for this problem. (1 mark) (b) Use graphical analysis, draw the graph and solve the model. (1 mark) (c) How many Butter cake and Cupcake to make in order to maximize the profit? (1 mark)