I have 7 hectares of land in the Philippines which can be planted to rice (X1) and/or corn (X2). I also have 72 days of labor and 72 tons of fertilizer.
One hectare of rice requires 6 days f labor and 12 tons of fertilizer. One hectare of corn requires 12 days of labor and 6 tons of fertilizer. The cost of water is $10 per ton, labor is $20 per day, and land can be rented for $10 per cropping season.
One hectare of rice can produce 3 tons which can be sold for $150 per ton. One hectare of corn can produce 5 tons which can be sold for $120 per ton.
Using graphic analysis:
1. State the objective function
2. State the constraint functions
3. Find the optimum number of hectares that must be planted to rice or corn to maximize
4. Estimate the maximum profit
Using the computer, validate you answers to questions 3 and 4 above.
A Complete, Neat and Step-by-step Solution is provided in the attached Excel file.
Linear Programming: Modeling Examples
A publishing house publishes three weekly magazines-daily life, agriculture today, and surf's up. Publication of one issue of each of the magazines requires the following amounts of production time and paper:
Production (hr.) Paper (lbs.)
Daily Life 0.01 0.2
Agriculture Today 0.03 0.5
Surf's Up 0.02 0.3
Each week the publisher has available 120 hours of production time and 3,000 pounds of paper. Total circulation for all three magazines must exceed 5,000 issues per week if the company is to keep its advertisers. The selling price per issue is $2.25 for daily life, $4.00 for agriculture today, and $1.50 for surf's up. Based on past sales, the publisher knows that the maximum weekly demand for daily life is 3,000 issues; for agriculture today, 2,000 issues; and for surf's up, 6,000 issues. The production manager wants to know the number of issues of each magazine to produce weekly in order to maximize total sales revenue.
a. formulate a linear programming model for this problem
b. solve the model by using the computer (excel)