AboutChen Min Expertise All the conceptual questions except for probabilities and statistics are welcomed.
I am good at answering your algebra (including logarithm, functions, trigonometry) and geometry questions.
I can also provide to you a firm understanding into calculus and other mathematical ideas and concepts.
You can either ask questions in English or Chinese.
Important:Please avoid asking me questions related to economics.After all, I am only a secondary school student
Experience A lot of participation in Math Olympiad Competition with numerous awards (Not always gold, though)
Question Find the minimum and maximum values of z = 3x + 4y for each of the following sets of constraints.
x + y <or equal to 6
-x+ y <or equal to 2
2x- y <or equal to 8
Answer Obviously your single constraint is far from enough.
Hence I assume one more constraint,i.e.x>0 and y>0
Linear programming can be solved using Cartesian coordinates, which is the easiest approach.
For example, you can express the inequality: x - y > 8 by drawing a line y - x + 8 = 0.(Notice I put a positive y on the left). Any point above the line(not on the line!)will surely have coordinates satisfying the inequality, so the inequality can be expressed as the AREA above the line.(IMPORTANT:if the inequality is a "<", it should be the area below)
Now you can find the max and min with an inequality as constraint.
Notice that your max and min values must have x and y falling exactly into the above-mentioned area.
Now draw a line 3x + 4y = 0.It will leave a segment inside the region.(Otherwise there is no solution)In order to find the maximum, you shift this line up, until it is about to move out of the region.Note the y-intercept of this line,it is the max of z.Similarly, you obtain the minimum by shift down. If you can't move the line "out",then there is no max or min.
I'm sure you'll be able to find the answer yourself:)After all, getting answers is only significant when you do it yourself!
