Group Case Problem #$1$

Many businesses are moving to the Internet for many of its supply transactions, creating web sites where it will interact with its suppliers. In technical terms, this is often referred to as business$-$to$-$business $($B$2$B$)$ electronic commerce. Research this activity and provide a report discussing it$.$ In your report, you should identify at least three companies that are either already operating in a B$2$B mode or are developing such an operation. Your report should include an introductory overview between $2-3$ pages, double$-$spaced, Arial or Times Roman font size $12,1-$inch margin on all sides. Your introductory overview should include the benefits, costs, and risks associated with this type of operation. Your introductory overview should also include a brief discussion of how different companies are using B$2$B in their practices. Focus on the companies you researched and discuss in the remainder of the report. The remainder of the report should also include a more detailed discussion of each company and how it is using B$2$B in its operations. Your discussion of each company that you researched does not need to be longer than $1$ or $2$ pages per company. Please include a page of references.

Group Case Problem #$2$

Margaret Young$$s family owns five parcels of farmland broken into a southeast sector, north sector, northwest sector, west sector, and southwest sector. Young is involved primarily in growing wheat, alfalfa, and barley crops and is currently preparing her production plan for next year. The Pennsylvania Water Authority has just announced its yearly water allotment, with the Young farm receiving $7,400$ acre$-$feet. Each parcel can only tolerate a specified amount of irrigation per growing season as specified in the following table:

Parcel

Area $($Acres$)$ Water Irrigation Limit $($Acre$-$feet$)$

Southeast $2,0003,200$

North $2,3003,400$

Northwest $600800$

West $1,100500$

Southwest $500600$

Each of Young$$s crops needs a minimum amount of water per acre, and there is a projected limit on sales of each crop. Crop data follow.

Crop Maximum Sales Water Needed Per Acre $($Acre$-$feet$)$

Wheat $110,000$ bushels $1\mathrm{.}6$

Alfalfa $1,800$ tons $2\mathrm{.}9$

Barley $2,200$ tons $3\mathrm{.}5$

One acre of land yields an average of $1\mathrm{.}5$ tons of alfalfa and $2\mathrm{.}2$ tons of barley. The wheat yield is approximately $50$ bushels per acre. Young$$s best estimate is that she can sell wheat at a net profit of $$2$ per bushel, alfalfa at $$40$ per ton, and barley at $$40$ per ton. The wheat yield is approximately $50$ bushels per acre.

Write the objective function and constraints for the linear programming problem if we want to maximize the profit? What is the solution to this linear programming problem?