3. NASA conducts 3 different types of experiments on their missions and each experiment pro- duces a different number of thermal readings, chemical readings, and physical specimens. Additionally, each experiment costs a different amount to perform. The data for each type of experiment is listed in the following table. Experiment Thermal Readings Chemical Readings Physical Specimens Experiment Cost Atmospheric Scan 2 2 0 $10,000 Robotic Landing 4 3 3 $15 million Astronaut Landing 3 4 6 $30 million For NASA's next space mission they want to collect at least 100 thermal readings, 30 physical geological specimens, and 50 chemical readings while minimizing the total cost of experiments. How many of each type of experiment should NASA perform and what will the total experi- mental cost be? (a) (1 pt) Identify the goal. (b) (3 pts) Define the variables used in this problem. (c) (6 pts) Identify the objective function and constraining equations and use them to write down the full linear programming problem. (d) (15 pts) Solve the linear programming problem using the Simplex method. Every step of the Simplex method does not need to be shown in your report. You do need to write down the starting tableau and identify the first pivot element. Then write down the final Simplex tableau. (e) (5 pts) Interpret the solution in the context of the problem. How many of each type of experiment should NASA perform to meet their requirements and minimize cost? What will the total experimental cost be? After performing the needed experiments, will NASA have gathered any extra thermal readings, chemical readings, or physical specimens above the minimum amount they want to collect