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Falkqwer
Question
I just noticed the last line: If you must order at least one of each type of table, because without that line I was not getting any of your choices. Can you try to sketch the relations? Let x be the number of type A and y be the number of type B You can order no more than 190 tables this month. that means the sum of x and y must be less than or equal to 190 x+y≤ 190 put this into slope-intercept form: y ≤ -x + 190 plot the line y= -x + 190 shade the area under this line (this is where y is less than the line) can you do that?
It only shows a bit of the graph. By hand: |dw:1358269570252:dw|
OK so what does this tell me now? sorry I'm dumb :(
We don't go below x=0 (we can't order less than 0) same for y that triangle represents all (x,y) pairs of orders where x+y ≤ 190 (and x+y≥0 we can't order less than 0) if you go outside the triangle you will order too many or a negative number. Neither is allowed.
you need to make at least $4,610 profit on them It would be good if you could write down the relation (mathematical expression) for this. Hero posted it, but you should try. The profit will be the number of type A's times the profit per type A plus # of B's times profit of a B this sum must be ≥ 4610 Can you write down the expression?
ok, but use x and y, because we have to plot this...
ok :) 29x + 19y >_4610
can you put it into slope-intercept form?
slope intercept form is y ≥ mx + b in other words, y is by itself on the left. First step is add -29x to both sides. Just write -29x on both sides what do you get?
don't make things up. start with 29x + 19y >= 4610 write -29x on both sides: -29x + 29x + 19y >= -29x + 4610 on the left side you have 29x and -29x (think: 29 x's take away 29 x's. I get no x's) 19y ≥ -29x +4610 now divide both sides by 19. That means divide each term on both sides by 19 what do you get?
I assume that 12 is a typo?
now, let's change into decimals (only a few digits). Roughly we get y ≥ -1.53 x + 242.6 now plot this line. Y ≥ means shade all the Y above the line. Can you plot this line?
for y ≥ -1.53 x + 242.6 we first plot y = -1.53x +242.6 if we set x to 0, what is y ?
Ok, x=0, y = 242.6 (0,242.6) is one point on the line can you plot this point ?
yes, that looks good See http://www.khanacademy.org/math/algebra/linear-equations-and-inequalitie/coordinate-plane/v/plot-ordered-pairs if you need a refresher. now lets find y when x = 100 y = -1.53x +242.6 replace x with 100 y = -1.53*100 + 242.6 what do you get ?
I picked x=100 because it is easy to multiply by 100. we could pick any x, but x near or inside our triangle makes sense.
-1.53*100 is a negative number. try again
that means (100,89.6) is on the line. can you plot this point ? go to x=100 and move up about 90.
now connect the dots (or x's in this case) |dw:1358272145701:dw|
d.)100 of type A; 90 of type B
I shaded the area above the line, because that is where y ≥ to the line The black shaded area is everywhere where you get the needed profit (remember profit must be ≥ 4610) We also must be below the red line. To meet both requirements, we must be in the lower triangle.
ahhhh ok I'm confused now...what is the answer?
Once you get the "feasible" region, you check the "corners" for the (x,y) pair that matches your requirement. In this case, the bottom two spots have y=0 and the statement If you must order at least one of each type of table means we can rule out those points we have to find the intersection of the two lines. but we see by eyeball it is 100, 90
A is x in our graph. and B is y Here is how to find where the lines cross: you start with y= -x + 190 y = -1.53x +242.6 when they meet they have the same y values. we set -x + 190 = -1.53x +242.6 add 1.53x to both sides (you should learn how to do this, btw) 1.53x - 1x + 190= -1.53x + 1.53x +242.6 on the left we get 0.53x+190 and on the right 242.6: 0.53x +190 = 242.6 add -190 to both sides 0.53x +190-190= 242.6-190 0.53x = 52.6 divide both sides by 0.53, and x = 99.2 looking at our graph, we want x bigger than this (we have to buy a whole table) x=100 and x+y =190 replace x with 100: 100+y=190 add -100 to both sides: 100-100+y= 190-100 y=90 In a harder problem, we would use these x,y numbers in the cost equation, and find the (x,y) pair (of the three corners) that gives the lowest cost. here, we just need to find the top "corner" because the bottom 2 are ruled out by the question (we must buy some of both types, so 0 is not allowed)
So the answer is A :) thank you so much for spending the time on teaching me :p I really appreciated
I think you can do this stuff, but you have skimped so much in learning all the details that it is difficult to do a problem like this where you have to remember how to do lots of things: plot, solve equations, etc.
Personally, I would pick just one area (example: putting equations into slope-intercept form), and watch a video at Khan
ok I'll try that thanx again :)