Question

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 that 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? Assuming that 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?
Bids by Companies (in $1000s) for Various Subcontract
Company
Component A B C D
1 185 225 193 207
2 200 190 175 225
3 330 320 315 300
4 375 389 425 445
What is an LP model that matches this?

Answer 1

Answer:

Following are the solution to the given question:

Step-by-step explanation:

Let $x_{ij}=1$ when i is the element itself is allocated to 'j' $i_0$

Min  

$185X_{1A}+225X_{1B} +193X_{1C} +207X_{1D} +200X_{2A} +190X_{2B} +175X_{2C}+225X_{2D}+330X_{3A} +320X_{3B} +315X_{3C}+300X_{3D}+375X_{4A}+389X_{4B}+425X_{4C}+ 445X_{4D}$

Subject to:

$X_{1A} +X_{1B}+X_{1C}+X_{1D}=1\\\\X_{2A} +X_{2B}+X_{2C}+X_{2D}=1\\\\X_{3A} +X_{3B}+X_{3C}+X_{3D}=1\\\\X_{4A} +X_{4B}+X_{4C}+X_{4D}=1\\\\X_{1A} +X_{2A}+X_{3A}+X_{4A}=1\\\\X_{1B} +X_{2B}+X_{3B}+X_{3B}=1\\\\X_{1C} +X_{2C}+X_{3C}+X_{4C}=1\\\\X_{1D} +X_{2D}+X_{3D}+X_{4D}=1$