Solve the following problems by using the inverse of the matrix involved.   ​(a) An automobile factory produces two​ models, A and B. Model A requires 1 labor hour to paint and 1/2 labor hour to​ polish; model B requires 1 labor hour for each process. During each hour that the assembly line is​ operating, there are 70 labor hours available for painting and 60 labor hours for polishing. How many of each model can be produced each hour if all the labor hours available are to be​ utilized?   ​(b) Suppose each model A requires 10 widgets and 14 shims and each model B requires 7 widgets and 10 shims. The factory can obtain 730 widgets and1030 shims each hour. How many cars of each model can it produce while using all the parts​ available?   Is 20 and 60 correct for a. and b= 45 and 60?

College Algebra (MindTap Course List)
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Solve the following problems by using the inverse of the matrix involved.
 
​(a) An automobile factory produces two​ models, A and B. Model A requires
1 labor hour to paint and 1/2 labor hour to​ polish; model B requires 1 labor hour for each process. During each hour that the assembly line is​ operating, there are 70 labor hours available for painting and
60 labor hours for polishing. How many of each model can be produced each hour if all the labor hours available are to be​ utilized?
 
​(b) Suppose each model A requires 10 widgets and 14 shims and each model B requires 7 widgets and 10 shims. The factory can obtain 730 widgets and1030 shims each hour. How many cars of each model can it produce while using all the parts​ available?
 
Is 20 and 60 correct for a. and b= 45 and 60?
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