Use Matlab to solve the problem below by using det(A) and invdet(A) builtin functions and a control structure that will be plotted if there are infinitely many solutions.

Product 1 Product 2 Product 3 Hours Reactor A Reactor B The table shows how many hours it takes reactors A and B to produce a ton of each product. From the table we see that for every ton of product 1 produced we need to run Reactor A for 5 hours and also run Reactor B for 3 hours. The two reactors are available for 40 hours and 30 hours per week respectively. Management makes sure that the reactors run the maximum number of available hours every week. Using the table above, we see that the amount (in tons) of product 1, pi, product 2, p2, and product 3, p3 that are produced in a week must satisfy the following two equations 1) 5 p, t 3 p2 +3 p3 40 2) 3 pi t3 p2 4 p3 30 Let Fi, F2, F3 represent the profit for a ton of each product. Then the total weekly profit, PW, is given by: Create a script M-file that solves for and displays the values of Pi, P2, and P3 given the required weekly profit, PW, and values for Fi, F2, and F3 as inputs from the Command Window. Test your solution for the following three cases Casel: Fl= $400, F2-5600, F,-$150, and weekly profit PW= $4,000 Case 2: Fl= $400, F,-$300, F,-$350, and weekly profit PW= $4,000 Case 3: F1$550, F2 $450, F $550, and weekly profit PW $5,000 Any problems in calculating the output should result in a meaningful error message. If there is more than one solution, generate a plot of the possible production mixes