Overview
Module 4 Assignment
Questions to answer
- Make a sheet called “Question 1”.A farmer in Iowa owns 45 acres of land.He is going to plant his land with either wheat or corn (any combination is allowed).Each acre planted with wheat yields $200 profit, requires 3 workers and requires 2 tons of fertilizer.Each acre planted with corn yields $300 profit, requires 2 workers and requires 4 tons of fertilizer.The farmer has 100 workers an 120 tons of fertilizer available.
- How many acres should the farmer devote to each crop?
- What is the profit the farmer will realize with this solution?
- Which constraints are binding?
- After you have found the optimal solution to Question 1, re-run Solver to obtain the Sensitivity Report.Change the name of the sheet of the Sensitivity report to “Question 2”.Use this Sensitivity report to answer these questions in a text box on the Question 2 sheet::
- The neighboring farmer offers to sell one acre of land to our farmer.How much should our farmer be willing to pay for this acre?
- A worker comes to the farmer’s door and offers his labor.How much should the farmer be willing to pay for this worker?
- Go back to the Question 1 sheet.Change the model to have 101 workers available.Resolve the problem (no Sensitivity report).What is the new solution in terms of acres used and objective function?Does this result match the value found in question 2b?
- Make a sheet called “Question 3”.Tigers Brewery (a wholly-owned subsidiary of the IE department! – just kidding!) produces beer and ale.Beer sells for $5 a barrel during football season and ale sells for $2 per barrel.Producing a barrel of beer requires 5 pounds of malt and 2 pounds of hops.Producing a barrel of ale requires 2 pounds of corn and 1 pound of hops.The brewery has 50 pounds of malt, 60 pounds of corn and 25 pounds of hops.
- How many barrels of each type of beverage should Tigers Brewery make?
- What is the profit Tigers Brewery will realize with this solution?
- Which constraints are binding?Without running the sensitivity report, can you guess which constraints will have shadow prices of 0?
Formulate this as a linear program.Implement your linear program in the Question 1 sheet.Solve this linear program using Solver.
In a text box, answer these questions:
Formulate this as a linear program.Implement your linear program in the Question 3 sheet.Solve this linear program using Solver.
In a text box, answer these questions: