How can i solve Linear Programming word problems?
My Algebra 3-4 class is currently learning how to do Linear Programming. I get the basics of it, but when it comes to word problems, i just want to rip my hair out of my head!!!
I need to find a way how to solve word problems that uses Linear Programming so that I can understand it a lot better!
Here’s an example problem that I’m struggling with:
A farming cooperative mixes two brands of cattle feed. Brand X costs $25 per bag and contains two units of nutritional element A, two units of element B, and two units of element C. Brand Y costs $20 per bag and contains one unit of nutritional element A, nine units of element B, and three units of element C. The minimum requirements of nutrients A, B, and C are 12 units, 36 units, and 24 units, respectively. What is the optimal number of bags of each brand that should be mixed? What is the optimal cost?
Thanks in advance!!
These can be solved by graphing. You graph the different inequalities on the same set of axes, The maximum and minimum will occur at one of the vertices of the shaded polygon you get from all the intersecting lines. So find those coordinates and plug them into the formula you want to maximize or minimize. So for this,
let x = bags of brand X and y = bags of brand Y. Your constraints are
2x + 1y ≥ 12 [this comes from the needs for element A]
2x + 9y ≥ 36 [from element B]
2x + 3y ≥ 24
x ≥ 0
y ≥ 0
So graph those boundary lines, shade, and see where the vertices of the resulting polygon are. The cost equation which you want to minimize (optimize) is
C = 25x + 20y so plug the coordinates of the vertices in there and see which gives the lowest cost.
Hope that is what you needed to know…
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