Asmall manufacturing firm has decided to expand production capacity by adding four machines: (1) a punch press, (2) a grinder, (3) a lathe, and (4) a welding machine. there are only four possible locations: a, b, c, and d. the welding machine will not fit in location b. the material handling costs of locating each of the machines in each of the possible locations are expressed in terms of dollars per hour (where m represents an arbitrarily large cost):

abcd are locations and 1234 are machines

a b c d
1 94 13 62 71
2 62 19 84 96
3 75 88 18 80
4 11 m 81 21

a. what is the optimal assignment of machines to locations?
b. what is the cost associated with the optimal assignment from part a?