A farmer acquired 290 acres of land to grow wheat, barley and/or rye. The farmer has a budget of 4 $50,000 and a workforce available of 6400 hours for the season. Costs, profits, and labor requirements 5 are as follows: Cost ($/acre) Profit ($/acre) Labor (hours/acre)
Wheat 122 45 12
Barley 185 82 18
Rye 146 61 16
The farmer has a contract to supply wheat to a local client for the equivalent of 45 acres of wheat 12 production. Due to limited demand, a marketing study recommended that no more than 100 acres 13 should be utilized for each product during the season.
The objective is to determine the number of acres to grow wheat, barley and rye to maximize total profit 15 given the constraints.
3 points Enter Formulation in yellow cells below
Objective Function
Subject to:
Constraint 1
Constraint 2
Constraint 3
Constraint 4
Constraint 5
Constraint 6
Constraint 7
Constraint 8
Set up the problem on a different sheet
Constraint 4
Constraint 5
Constraint 6
Constraint 7
Constraint 8
1 point Set up the problem on a different sheet
1 point Solve the problem using SOLVER, making sure to generate the Answer Report and Sensitivity Report
1 point How much is the total profit?
1 point The farmer is considering either buying more land or increasing his budget. What would you recommend?
Buy more land <--- enter 'Yes' or 'No' If 'Yes', how much more? Increase budget <--- enter 'Yes' or 'No' If 'Yes', how much more? <--- enter the number of acres to buy <--- enter the amount ($) of budget increase 30 31 1 point 32 33 1 point 34 35 1 point 36 37 38 39 40 41 42 43 44 45 461 point 47
After the first season, the farmer was able to improve growing methods such that costs and profits are now:
Cost ($/acre) Profit ($/acre)
Wheat 113 49
Barley 170 88
Rye 134 75
1 point Set up the problem on a different sheet 48
1 point Solve the problem using SOLVER, making sure to generate the Answer Report and Sensitivity Report
1 point How much is the new total profit?