Please do not answer if you do not completely understand the question. for part a i need decision variables, objective function, and constraints.

thanks

Sphero produces toy robots for various companies. Before shipment, these robots undergo a quick test on one of three machines in Sphero's quality control department. Sphero has five types of robots, and any of the machines can be used to test any of the robot types. However, the time required for testing on each machine depends on the robot type, as shown in the following table: Machine 1 2 3 Alpha 3 5 2 Processing time in minutes Robot type Beta Gamma Delta 4 4 5 3 5 4 5 3 3 Nuw Epsilon 3 5 4 Today, Sphero's quality control department has 80 Alpha robots, 75 Beta robots, 80 Gamma robots, 120 Delta robots, and 60 Epsilon robots that need to be checked. Each machine can be used for a maximum of 8 hours per day, and Sphero wants to determine how many of each robot type to test on each machine to as to minimize the total time used for testing (leaving as much time as possible for other tasks the department has to perform) a) Formulate a Linear Programming model for this problem. Clearly define the decision variables, the objective function, and the constraints. b) Create a spreadsheet model for this problem and solve it using Solver. What is the optimal solution? c) Suppose now that Sphero's quality control department wants to make sure that each machine is used approximately the same amount of time. How will this impact the optimal solution