Friday, May 22, 2009
Thursday, May 7, 2009
One problem when people usually meet in shopping is what people should buy in “clearance sale” with aim to sale again. Usually people confuse to buy between/among two types of products or more. The objective of this problem usually is maximize profit, but this problem will be more difficult because people should decide among different constraints such as sales demand, budget, and capacity. How do we solve this problem?
Solving of this problem will become simple with Linear Programming (LP). LP is a mathematical technique for optimization of linear objective function. In 1939, Leonid Kantorovich, a Russian mathematician, founds this technique. Then, George B. Datzig, John von Neumann, Leonid Khaciyan, and Narendra Karmarkar develop this technique. Clearance sale shirt and t-shirt example below will show that LP can be used to solve this problem. For example, a department store opens New Year clearance sale for shirt and t-shirt. One shirt prices $25 and $15 for a t-shirt. A shop looks this opportunity to make a $400. In addition, his inventory only can keep 100 clothes, whereas he has kept 53 shirts and 29 t-shirts. Then, he considers that he can sell shirt at least twice than t-shirt in one week. How much shirt and t-shirt should he buy in this clearance sale?
Consider that X1 is for shirt and X2 is for t-shirt. The objective of this problem is maximize profit from (40-25) X1 + (35-15) X2 = 15 X1 + 20 X2. There are three constraint of this problem. First, sales demand constraint is X1 – 2X2 >= 0. Second, budget constraint is 25X1 +15 X2 <= 400. Third, capacity constraints is X1 + X2 <= (100-(53+29)) ~ 18. So the mathematical equation is:
Max Profit: z = 15X1 + 20 X2
Constraint: X1 – 2X2 >= 0
25X1 +15 X2 <= 400
X1 + X2 <= 18
There are many ways to solve this problem such as LP Graphic and Excel Solver. The graphic and the excel solver output will be showed below.
From graphics, there are three alternatives of optimum solutions. First, in point (18, 0) will make profit $270. Second, in point (13, 5) will make profit $295. Third, in point (12.3, 6.15) will make profit $307.5, but this answer is invisible because shirt and t-shirt cannot be decimal. Hence, the nearest options are (12, 6) with profit $300. Furthermore, He should buy 12 shirts and 6 t-shirts. It is very suitable with the answer from Excel Solver table below.
The owner of shop also can analyze the changing in the parameters of this LP problem. This analysis is called sensitivity analysis. In this case, Excel Solver is also used to define the sensitivity analysis.
The table above shows that the final answer will not be change if:
1. The profit of Shirt changes in range from 0 to 20 infinity
2. The profit of T-Shirt changes in range from 15 to infinity
3. The constraint of budget change in range from 290 to infinity
4. The constraint of capacity change in range from 0 to 18.461538462
5. The constraint of demand change in range from -36 to 3
Hence, have fun in shopping.
Wednesday, April 22, 2009
Save electricity, save fuel, and save forest are example activities to save energy. Save electricity activities, such as turn off lamp, air conditioner, and electronic equipment if it is not really used, will reduce greenhouse effect. Other activity to support it is save fossil fuel like mineral oil (kerosene, paraffin waxes, gasoline, diesel, and petroleum), gas, and coal. The output of combustion are greenhouse gas emissions air pollutants such as carbon dioxide (CO2), methane (CH4), nitrogen oxide (NO), nitrogen dioxide (NO2), sulphur dioxide (SO2), volatile organic compounds, and heavy metals. In addition the other activity to reduce greenhouse effect is save forest because forest as earth’s lung function to reduce greenhouse effect. Forest will convert greenhouse gas emission into Oxygen (O2). Forestation and forbid illegal logging are the best activities to save our earth.
What should all earth’s citizens do? To save this earth, the simplest activity is to clean environment such as no littering, clean water resources, and manage wastes. First, no littering culture everywhere must develop among people because this simple activity can help to clean our earth. Second, clean water resources like gutter, lake, river, swamp, basin, and sea. Ideally, all water resources are free from rubbish and waste. Then, citizens, industry, and government need to pay attention about this. Third, the other simple activity is managing wastes with 3R (Reduce, Reuse, and Recycle). 3R means cut down rubbish and waste, exploit it which are still good to use, and produce it into new product.
The important activity to save our earth is from people themselves with healthy life style habit. Consume healthy food have two benefits. Beside good for health of the people themselves, it can affect psychologically to aware with healthy earth. Consume healthy food will not be complete if people do not want to do activity sports. Sport awareness also concern psychologically to make the earth green because in sport need oxide from plant. Healthy habits are also important to save the earth. It include not to smoke because smoking produce air pollutant like carbon dioxide, clean body and environment routine, and reduce in using plastics and paper.
“Global Warming” is a disaster that majority caused by human. Hence, they should improve the quality of earth. Saving energy and cleaning the earth with healthy life style habit are important activities which need supported from all citizen of earth. Then, HAPPY EARTH DAY 22 April, SAVE OUR EARTH.