Question

For each problem, you must:
1. Define the variables
2. Write the function to be maximized or minimized.
3. Write a system of inequalities.
4. Graph and write the vertices of the feasible region.
5. Solve the problem and answer the question.

4. Redbox is making copies of movies for their vending locations. They're making regular DVDs as well as Blu-Ray DVDs. Each regular DVD requires 4 minutes of recording time and generates a profit of $9, and each Blue-Ray DVD requires 6 minutes of recording time and generates a profit of $8. The Recording machine runs at most 12 hours a day. Because of demand, the company manufactures at least twice as many Blu-ray DVDs as regular DVDs. What's the maximum profit that can be generated in 1 day?

Answer 1

@TuringTest Give this a look! See if you can help, I cannot figure it out!

Answer 2

@TuringTest Do you get it dude???

Answer 3

oh I was not even really looking
okay let me see here...

Answer 4

let x=DVD's and y=Blu-Ray

Answer 5

12 hours is 720 minutes, so\[4x+6y\le720\]

Answer 6

profit is given by price*number of DVD's, so the function is\[P=9x+8y\]

Answer 7

"Because of demand, the company manufactures at least twice as many Blu-ray DVDs as regular DVDs. "
we can write this as\[y\ge2x\]

Answer 8

graph the two inequalities, you should be able to do that

Answer 9

\[y\ge2x\]\[y\le-\frac23x+120\]therefore\[2x\le y\le-\frac23x+120\]graph this region

Answer 10

what's 5

Answer 11

the hard one, let me think on that

Answer 12

yea @TuringTest

Answer 13

Is this calculus or algebra?

Answer 14

Label your work from 1 - 5, so I know what goes with what

Answer 15

You are supposed to be doing this along with me. This site is not about giving away answers, though I have been rather generous about that up till now. If you can't figure out what goes with what then you need to step back and review earlier material.

Answer 16

It confuses me when it's not numbered

Answer 17

my advice for maximizing the profit is to graph the region described by the inequalities that I gave you, and check each vertex. plug the x and y values from each vertex into the profit function I wrote, and see which is the highest.

Answer 18

do you really have a problem telling me what the variables in this case are? I basically did each step in order.

Answer 19

Here's what I think:
2. 4x + 6y < = 720
3. P = 9x + 8y

Answer 20

2. asks for the thing to be maximized, and the question asks you to maximize profit. Which function is that?

Answer 21

9x + 8y

Answer 22

yes, be sure to write the P= part though

Answer 23

the next part asks for the *system* of inequalities
there are two, write them both

Answer 24

y≥2x
y≤−23x+120

Answer 25

that second one is a fraction -2/3 I know
so yeah that's right

Answer 26

so then I would graph those 2 on my calculator

Answer 27

or with your hand, even better

Answer 28

do you know about the window on the calculator TI-84

Answer 29

something like this
no, I know how to do it by hand

Answer 30

I don't use graphing calculators unless circumstances are really ugly numbers; they hide too much of the actual math and impede understanding in my opinion

Answer 31

is the point (4,4)

Answer 32

here it's pretty easy because the boundaries are straight lines
find the y-intercepts, where the graphs intersect, and shade above and below the lines according to the inequality sign

Answer 33

what point?

Answer 34

is there 1 vertice

Answer 35

actually there are 3, but I know which one you mean

Answer 36

I only see one

Answer 37

what are the vertices then, because I don't want to be wrong

Answer 38

to find the vertex on the right solve the system of the two lines for x (that is where the two lines are equal, i.e. cross each other)

Answer 39

@TuringTest, because I am not for sure. I said (4,4)

Answer 40

solve the equation for x
show your work
2(4) is not equal to -(2/3)(4)+120

Answer 41

This part I just can't do for you, if you can't solve
2x=-(2/3)x+120
for x you have been slacking in class and need to review some basics

Answer 42

why are there 2Xs

Answer 43

because there are two lines

Answer 44

I mean in the problem

Answer 45

Thanks @TuringTest