(e) (8 pts) Using a matrix inverse, solve for the needed production levels of each sector. You may compute the needed matrix inverse with the online matrix tool, round to 2 significant figures. (f) (2 pts) Using a matrix inverse, solve for the needed production levels of each sector if NASA needs to instead meet demand for $230 million of robotics products, $110 million of computer science products, and $200 million of energy products. Round to 2 significant figures. (g) (2 pts) Using a matrix inverse, solve for the needed production levels of each sector if NASA needs to instead meet demand for $250 million of robotics products, $120 million of computer science products, and $210 million of energy products. Round to 2 significant figures. (h) (3 pts) Why is it beneficial to use a matrix inverse to solve this problem instead of using a Gauss-Jordan reduction process?Project Assignment The National Aeronautics and Space Administration, U.S.A. (NASA) has hired you as a consultant to help them analyze their various sectors of industry and solve some space flight problems. 1. In 2020, NASA tracked its input and output from their robotics, computer science (CS), and energy departments given in the following table measured in millions of U.S. dollars. Sector Robotics Used CS Used Energy Used Units Produced Robotics 60 10 20 200 Computer Science 10 30 10 80 Energy 50 15 20 150 From the data in the above table, determine the production levels of each sector needed to meet demand for $220 million of robotics products, $100 million of computer science products, and $180 million of energy products. Round to 2 significant figures. (a) (1 pt) Identify the goal. (b) (3 pts) Define the variables used in this problem. (c) (6 pts) Identify the constraining equations. (d) (5 pts) Write the constraining equations in matrix form. Define the technology matrix A and interpret the A2,3 and A1,2 entries. (e) (8 pts) Using a matrix inverse, solve for the needed production levels of each sector. You may compute the needed matrix inverse with the online matrix tool, round to 2 significant figures. (f) (2 pts) Using a matrix inverse, solve for the needed production levels of each sector if NASA needs to instead meet demand for $230 million of robotics products, $110 million of computer science products, and $200 million of energy products. Round to 2 significant figures.Problem Points Deliverables la Complete sentence identifying the goal. 1b Identify and define each variable for this problem. 1c Write the constraining equations using your defined variables. 1d 5 Write a matrix equation equivalent to the constraining equations. Define the matrix A. Interpret A2,3 and A1,2 in complete sentences. le 8 Define the matrix inverse needed to solve the matrix equation. Solve the equation using the matrix inverse and round to 2 significant figures. If 2 Solve the modified matrix equation using the matrix inverse and round to 2 significant figures. 1g 2 Solve the modified matrix equation using the matrix inverse and round to 2 significant figures. 1h 3 Complete sentence response of your thoughts. Table 1: Rubric for problem 1