A shop has 4 machinists to be assigned to four machines. The hourly cost of having each machine managed by each machinist is as follows:

Machine 
Machinist 
A 
B 
C 
D 
1 
$10 
$2 
$8 
$6 
2 
9 
5 
11 
9 
3 
12 
7 
14 
14 
4 
3 
1 
4 
2 
a. Formulate a linear programming model for this problem.
b. Find out the optimal assignment and compute total minimum cost.