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