WORD PROBLEMS SUCK

[Breepop]

..and I have 10 of them to do for a test grade! I've done 6 by myself (and I can't even express how happy I am about this), but the other four... uh.

Normally I'd go to Academic Support at my college for this, but I literally have no time (it's due Tuesday and I have like 19 other things due that day). And apparently my friends in this course are having more trouble with this than I am. SO. YOU GUYS GET TO BE MY SUPPORT. Please? k.


10. A salesperson finds that her sales average 40 cases per store when she visits 20 stores each week. For every two additional stores she visits per week, the average sales per store decreases by one case. How many stores should she visit each week if she wants to maximize her total sales?

This is really the only one I'm completely lost on. IT DOESN'T SEEM LOGICAL. How does cases per store even relate to number of stores she visits? WHAT.

So, if someone could make this make sense, or help me set it up, I can probably do the rest.

^Done! Thanks bry4nmw!



9. The daily profit earned by the Sweets factory is related to the number of cases of candy canes produced in the following way: P(x) = -x² + 160x - 3400, where P(x) is the daily profit in dollars, and x is the number of cases of candy canes produced daily. How many cases of candy canes must be made daily in order to maximize the profit? What is the maximum daily profit? (Note: remember that maximum function value for a quadratic function can occur only at the vertex)

...I think I set this up correctly. It's the math I'm having trouble with. Well, kinda. I just used the quadratic formula on that P(x) thingy, but... I got two plausible answers? I expected one to be negative so I could cancel it, but they both ended up plausible. Unless I did something wrong. huh.

^Done! Thanks bry4nmw!



4. A salesperson is paid a commission of 6% on the first $20,000 in sales made each month and 10% on any amount over $20,000 in sales. Express the salesperson's montly commision, C, as a function of the monthly sales, s. (Note: This will be a split function.) If monthly sales total $18,250, how much is the commission? If monthly sales total $24,750, how much is the comission? Graph this function.

I'm having trouble with the graph on this one. I have everything else. I just need an idea of what it should look like... I have one, but I guessed. The graph seems too simple. Maybe I have it correct, and I'm only questioning because it was so easy? But I don't think so. YEAH.




2. Maggie moved into a new house and was planning how to design the ayrd. Sitting on the front steps one day, she visualized a triangular flower bed, with one side along the right-hand edge of the straight front sidewalk (as viewed from her vantage point on the steps). The edge of the flowerbed closest to the house would start 2 feet from the steps, and would slope at a rate of 2 feet toward the street for every 3 feet to the right. The far edge of the triangle would begin at the edge of the sidewalk 9 feet from the steps. This side would slope at a rate of 1 foot toward the house for every 2 feet to the right. Help Maggie draw up her flowerbed plans by representing the edge of the sidewalk by the y-axis, the line containing the bottom edge of the bottom step as the x-axis, and the corner where the edge of the sidewalk meets the steps just below Maggie's right foot as she sits on the steps by the origin. This places the region where she wants the flowerbed in the first quadrant. Maggie wants to plant a dogwood tree at the corner of this triangular flowerbed where the two other sides meet.

a) Find an equation for each of the other two sides
b) Find the coordinates of their point of intersection
c) Graph the region
d) Find the area of this triangular flowerbed
e) Show the position of the dogwood tree on your graph


THIS ONE FUCKING SCARES ME. Where do I even start!? Just looking at this makes me want to cry. ;_;

^Done! Thanks Sean.





Uh, I realize I'm asking a forum mostly populated by people who more than likely haven't even taken pre-calc, but HEY, maybe we have ... a freakin' Daniel Biss. xD

[ElfLady]

I'm on it Bree! Have no fear!!! (or rather, have a bit less fear, the size of that bit determined by how much faith you possess in a 14 year old ADHD girl...)

[Sean S.]

You're in luck, I'm a physics major. I'll take the first one and here's a rough sketch of the last one. Hope it helps.

[Sean S.]

On 10)

Let's call
C the number of cases per store,
S the number of stores visited,
and
T the total number of cases.

T=C*S

But they say that C depends on S. S is our independent variable that we are free to change.

So we need to find the relationship between C and S.

I made a table.

S C
20 40
22 39
24 38
26 37

So find an equation that is C = f(S)

C= 40-(S-20)/2

Then plug that into T=C*S, so that you have T only be a function of S.

T= S*[40-(S-20)/2)]

Then take the derivative and find the maximum.

[Breepop]

Apr 16, 2010 22:29:38 GMT -5 Sean S. said:

here's a rough sketch of the last one. Hope it helps.

Woooooooooow, that helped a lot. Thanks so much. That problem turned out to be a lot easier than it looked. xd

One question though. Would the dogwood tree just be at the intersection of the edge closest to the house and the edge farthest from the house? It just says "where the two other sides meet." >.>

I think I might need some sleep before attempting #10 again. I still don't .. really understand it. xD I'll try that again in the morning.

P.S. Maggie is a freaking noob. Who puts a random triangular flower bed on one side of their yard? A NOOB THAT'S WHO. >:[

[speedlearner]

I have word problems and solutions on my channel, if you want to check them out. And by all means give me your future word problems. I'll see what I can do to help you in the future. http://www.youtube.com\user\speedlearner

[Jub]

Well for number 9. I think you're calculating the roots, not the vertex.
You could try graphing it on a calculator if you have a Ti with you.

[Jub]

Jub finished his algebra and solved for you. Number 9. 80 candy canes produce $3000 daily. Resources - Brain/Ti-84 Plus. Tell me if you want an explanation.

[bry4nmw]

Sorry if this is to late, but still wanted to try and help

Question #10

SPOILER: Click to show

First thing I did was write the relationship between the numbers:

x represents the additional stores visited
y represents the amount of cases sold

y = (x + 20)(40 -0.5x)

minor explanation:
x + 20 represents the total amount of stores visited
40 - 0.5x represents the amount of cases sold at each store

Now we expand the equation to make it quadratic:

40x - 0.5x^2 + 800 - 10x

We simplify:

-0.5x^2 + 30x + 800

And now we want to change it to vertex form:

-0.5(x^2 - 60x) + 800
-0.5(x^2 - 60x + 900 - 900) + 800
-0.5(x^2 - 60x + 900) + 800 + 450
-0.5(x - 30)^2 + 1250

We changed the equation to vertex form to find the maximum which is 1250, which means 1250 is the maximum amount of cases that may be sold.
Now in order for y to equal 1250, -0.5(x - 30)^2 must equal 0.
To do this simply find the value which makes x - 30 = 0. You can easily solve this algebraical.

x = 30

An good observation to make is that the vertex's Y will always represent the maximum and its x represents how to get to that maximum.

The way I did this is I made x = the additional stores the saleswomen needs to visit so you need to add the original 20 she visits.
So the answer to the question would be the saleswomen needs to visit 50 stores to make her maximum sales.

P.S. This may not have been the way your teacher would have been looking for, as I usually solve things "improperly".

Question #9

SPOILER: Click to show

What I think you did wrong was you solved for the x-intercepts when what it wants you to do is find the vertex equation. In that equation the constant number will be the maximum. The constant being the number at the end of the equation.

Sorry I didn't take the time to solve anymore, but I have trouble explaining things properly, so it takes me a small chunk of time to compose an understandable solution.