Considering the following LP model, What is the Objective Function (maximize profit) for this LP model? What are the constraints for this model (e.g. plastic constraints, Metal Constraints, Labor Constraints, Demand constraints, Non-negative constraints, etc...?). And what is the optimal solution for this LP model?

Topic: The management problem I would like to address that can be represented and solved as a linear programming model is production planning. In this scenario, the objective is to maximize the profit by determining the optimal number of units to be produced for each product type, given certain constraints such as available resources and demand. To show this, I will use the example of a toy manufacturer that produces three types of toys, toy cars, dolls, and barbies. The manufacturer will have a limited amount of plastic and metal available to produce the toys, as well as a limited amount of labor hours. These will be used as my constraints. The manufacturer can sell up to 1,000 toy cars, up to 800 dolls per week, and up to 900 barbies per week. The linear programming can be formulated as follows: Decision variables: P_CARS = number of toy cars produced per week P_DOLLS = number of dolls produced per week P_BARBIES = number of barbies produced per week S_CARS = number of car toys sold per week S_DOLLS = number of dolls sold per week S_BARBIES = number of barbies sold per week