Case Solution Problem 3
As per the information given, profits per acre on various crops are as follows:
Profit per acre on wheat = 50 x 2 = $100
Profit per acre on Alfalfa = 1.5 x 40 = $60
Profit per acre on Barley = 2.2 x 40 = $88.
Suppose Young’s production plan for the next year is as follows:
Parcel
Cultivation Area (Acre)
Land Available
Wheat
Alfalfa
Barley
Southeast
2000
North
2300
Northwest
600
West
1100
Southwest
500
Total
6500
Total profit as per the production plan:
The objective function to be maximized is:
Constraints
On Land:
On Water Irrigation Limit:
Parcel
Water Irrigation
Required
Maximum capacity
Southeast
3200
North
3400
Northwest
800
West
500
Southwest
600
In addition maximum water available is 7400
The constraints are:
On Sales:
Per acre production
Total Production
Maximum Sales
Wheat
50 bushels
110,000
Alfalfa
1.5 tons
1800
Barley
2.2 tons
2200
Constraints:
Thus mathematical model is:
Maximize:
Subject to:
Solving the problem using solver of MS Excel we get the solution as follows:
Variable
Solution
547.21
544.90
422.71
311.34
373.84
65.52
65.52
0.00
Variable
Max. Profit
Solution
0.00
0.00
586.66
376.95
35.33
0.53
0.53
315862.07
Crop Plan
Parcel
Cultivation Area (Acre)
Wheat
Alfalfa
Barley
Total Area
Southeast
547.21
65.52
586.66
1199.39
North
544.90
65.52
376.95
987.36
Northwest
422.71
0.00
35.33
458.04
West
311.34
0.00
0.53
311.87
Southwest
373.84
0.00
0.53
374.37
Profit
$220,000.00
$7,862.07
$88,000.00
$315,862.07
Profit per acre on wheat = 50 x 2 = $100
Profit per acre on Alfalfa = 1.5 x 40 = $60
Profit per acre on Barley = 2.2 x 40 = $88.
Suppose Young’s production plan for the next year is as follows:
Parcel
Cultivation Area (Acre)
Land Available
Wheat
Alfalfa
Barley
Southeast
2000
North
2300
Northwest
600
West
1100
Southwest
500
Total
6500
Total profit as per the production plan:
The objective function to be maximized is:
Constraints
On Land:
On Water Irrigation Limit:
Parcel
Water Irrigation
Required
Maximum capacity
Southeast
3200
North
3400
Northwest
800
West
500
Southwest
600
In addition maximum water available is 7400
The constraints are:
On Sales:
Per acre production
Total Production
Maximum Sales
Wheat
50 bushels
110,000
Alfalfa
1.5 tons
1800
Barley
2.2 tons
2200
Constraints:
Thus mathematical model is:
Maximize:
Subject to:
Solving the problem using solver of MS Excel we get the solution as follows:
Variable
Solution
547.21
544.90
422.71
311.34
373.84
65.52
65.52
0.00
Variable
Max. Profit
Solution
0.00
0.00
586.66
376.95
35.33
0.53
0.53
315862.07
Crop Plan
Parcel
Cultivation Area (Acre)
Wheat
Alfalfa
Barley
Total Area
Southeast
547.21
65.52
586.66
1199.39
North
544.90
65.52
376.95
987.36
Northwest
422.71
0.00
35.33
458.04
West
311.34
0.00
0.53
311.87
Southwest
373.84
0.00
0.53
374.37
Profit
$220,000.00
$7,862.07
$88,000.00
$315,862.07