1. A farmer has 1000 acres to be allocated among three crops. The number of person-hours per acre required for each corp and its profit per acre are given as follows.
Person-hour per acre
Crop A
Crop B
Crop C
3
5
4

Profit per acre
Crop A
Crop B
Crop C
$600
$300
$500

Ifthe farmer has at most 6000 person-hours available, determine the number of acres of each crop that should be planted to maximize the total profit.
  • Formulate this as a linear programming problem.
  • Use a spreadsheet to solve the problem.
2. A machine shop has one drill press and five milling machines, which are to be used to produce an assembly consisting of two parts, 1 and 2. The productivity of each machine for the two parts is given below:
Part
Drill
Mill
1
3 minutes
20 minutes
2
5 minutes
15 minutes

It is desired to maintain a balanced loading on all machines such that no machine runs more than 30 minutes per day longer than any other machine (assume that the milling load is split evenly among all five milling machines).
Divide the work time of each machine to obtain the maximum number of completed assemblies assuming an 8-hour working day.
Formulate this problem as linear programming problem.
Available from: Friday, 3 October 2008, 6:30 PM
Due date: Monday, 6 October 2008, 5:30 AM