optimazation problems.docx

Say you need to buy some new filing cabinets. You know that it is $10 per unit to buy Cabinet X, which holds 8 cubic feet of files and requires floor space of 6 square feet. On the other hand, it is $20 for every unit of Cabinet Y which requires floor space of 8 square feet and holds about 5 cubic feet of files. For this purchase, you have been given $140 but dont really have to spend all of it. The space in the office only has room for a maximum of seventy-two square feet of furniture. To maximize the volume of files you can store, how many of what model do you need to buy?The variables will then be:x= cabinet x purchased piecesy= cabinet y purchased piecesWhere:x>0 andy>0Because I need to consider the space allowed in the office and yet attempt to maximize volume of storage, the optimization equation will be the volume and the constraints will be floor space:Volume:v = 8x+ 12ySpace:6x+ 8y