I need step by step answers.

Show me the answers in both mathematical ( for example: maximize 2x+3y and related constraints) and in compact (matrix form) such as maximize cx subject to Ax b

ALSO DEFINE DECISION VARIABLES, PARAMETERS, OBJECTIVE FUNCTION , AND THE CONSTRAINTS

1. A bakery produces four different size cakes: small, medium, large, and extra large. The cakes require 3 steps: mixing, baking, and decorating. The amount of time it takes to complete each of these steps for each size cake is provided in the following table. Additionally, listed in this table is the profit earned from making each size cake. There is unlimited demand for small and large cakes each week, but only 5 medium cakes and 1 extra large cake are demanded each week. Assuming there are only 40 hours of mixing, baking, and decorating time available each week (4o hours for each task), how many cakes should the bakery make in order to maximize profit. Formulate this problem as a linear program by providing the decision variables, parameters/sets, model format 1 , model format 2 , and the description. Table 1: Summary of Data Note: Model format 1 uses numbers, such as, max:5x1+2x2, s.t. : x1+x210. Model format 2 uses vectors and matrices, such as, max:j=1ncjxj,s.t. : j=1naijxjbi,i=1,,m. When providing format 2 of model formulation, clearly define the vectors and matrices used