Chapter 6. Creative Robotics (CR) manufactures two lightweight robots designed for easier house-cleaning. The Alpha-ONE model is older, heavier, and is designed for carpet cleaning. The Alpha-TWO model is newer, lighter, and is designed primarily for wooden floor cleaning. The management team is trying to identify how to minimize their total costs of producing these two models. Their full-time workers consist of primarily manufacturing experts and about 3 people are required to commit themselves to manufacturing Alpha-ONE model and 4 for the Alpha-TWO model, per day. They have a total pool of 100 full-time workers now but are willing to hire more manufacturers if required. Similarly, the Alpha-TWO model is more complex and management has a pool of 20 part-time technical workers to help with the complexity, everyday. Again, they are willing to hire more part-time workers if required to assist with the Alpha-TWO model. As far as staff allocations for additional assistance in manufacturing Alpha-ONE and Alpha-TWO models, the expected number of individuals are 3 and 2 per day, respectively. The management has 58 people in their staff pool who can assist with the productions but has shown the willingness to hire more staff members if required. At the current time, they expect the cost of producing each Alpha-ONE model to be about $200 per day and each Alpha-TWO model to be $225 per day. Formulate a linear programming model that can be used to determine the number of units of each model that should be produced to minimize the total cost of producing them based on the labor force constraints. Write your linear program Equations in your answer file. You can either solve this problem graphically or by using Solver in Excel and then fill the blanks below:

1. Creative Robotics should produce Alpha-ONE Models and Alpha-TWO Models per day.
2. The Minimized Total Cost value is $ per day.
3. Based on the slack variables you obtained, do they need to hire additional workers? Answer Yes or No