please solve the problem with python

1. A local bakery produces three different types of cakes: 1-layer, which yields a profit of $15; 2-layer, which yields $20 profit; and 3-layer, which yields $10 profit, per cake. There are two main ingredients sugar and flour that each cake requires. The following table shows the number of cups of each ingredient needed for each type of cake. Cake 1 Sugar 1 Flour 2 2 3 Cake 2 4 1 Cake 3 3 2 The bakery has 60 cups of sugar and 45 cups of flour in stock. Formulate the LP for this problem, and then write out the LP in Matrix Form. Solve this problem using gurobi with python. Starting with your optimal solution to this problem, do the work by hand to answer each of the following questions (start with the original optimal solution for each question): (a) How much can the profit of a 1 layer cake change without the optimal solution changing? (b) If the profit for a 2-layer cake changes to $30, what is your optimal solution and objective function value? (c) If you only have 50 cups of sugar, what is your optimal solution and objective function value? (d) The bakery is considering adding cupcake boxes as the 4th type of cake. Each box requires 2 cups of sugar and 4 cups of flour, and yields a profit of $22. Should the bakery make cupcakes? If so, what is the new optimal solution and objective function value? (e) For one week the bakery is going to make everything pumpkin spice flavored. Cake 1 requires 0.5 tsp of pumpkin spice, Cake 2 requires 1 tsp, and cake 3 requires 1.5 tsp. There are 50 tsp of pumpkin spice available. Does the bakery need to change their baking plan for this week? If so, add the constraint to your LP in python and re-solve to find the new optimal solution and objective function value