A manufacturer of prefabricated homes has decided to subcontract four components of the homes. Several companies are interested in receiving this business, but none can handle more than one subcontract. The bids made by the companies for the various subcontracts are summarized in the following table.
Assuming all the companies can perform each subcontract equally well, to which company should each subcontract be assigned if the home manufacturer wants to minimize payments to the subcontractors? (Let
Ai = 1
if contract i is awarded to company A and 0 otherwise. Let
Bi = 1
if contract i is awarded to company B and 0 otherwise. Let
Ci = 1
if contract i is awarded to company C and 0 otherwise. Let
Di = 1
if contract i is awarded to company D and 0 otherwise.)