Question

I am trying to find the best way to Maximize my "companies" profit. I have two products that I sell. Produce at least 30 of product #1.
Produce at least 20 of product #2.
Product #1 costs $3 per unit to make.
Product #2 $5 per unit to make.
The total production cost cannot exceed $340.

If Product #1 earns a profit of $10 per unit and Product #2 earns a profit of $15 per unit, find the combination of Product #1 and Product #2 that will maximize profit.

Ive written out some inequalities to represent this. X is greater than or equal to 30. And y is greater than or equal to 20.

Answer 1

Cost of production cannot exceed $340, so, 3x+5y is less than or equal to 340. What combination of X and Y would maximize my profit?

Answer 2

I really need help on this. Im completely stumped.

Answer 3

There should be 3 points of intersection, I must graph and shade.

Answer 4

3x + 5y <= 340
x <= 30
y <= 20

product 1 (y) costs $3 to make with a $10 profit, leaving you with $7 per unit sold.
product 2 (x) costs $5 to make with a $15 profit, leaving you with $10 per unit sold
You make more selling product 2.

3x + 5y <= 340
3(30) + 5y <= 340
90 + 5y <= 340
5y <= 340 - 90
5y <= 250
y <= 25

I figure if you make more from selling product 2, then you want to sell the minimum of product 1, which is 30.

I cannot tell you the correct way to do this because I do not know.
But this way, your total profit is :
product 1 (x) .....selling 30 will make you (30 x 7) = 210
product 2 (y)....selling 25 will make you (25 x 10) = 250
250 + 210 = 460 (this is the total after the cost of materials has been subtracted)

Answer 5

sorry that I am not much help with the graphing

Answer 6

oops...the inequalities at the top should be y >= 30 and x >= 20.

Answer 7

@Hero ...are you good at these ??

Answer 8

oops....also product 1 is x and product 2 is y

Answer 9

@ganeshie8 ...help...am I way off on this ?

Answer 10

@satellite73 ....please help

Answer 11

I am trying to get someone to come and look at this

Answer 12

Thanks for the help Texaschic, i really need it. Id appreciate it if anyone was able and willing to answer this.

Answer 13

I do believe that (30,25) is one point

Answer 14

@Opcode ...help

Answer 15

@oldrin.bataku ...help please

Answer 16

bump the question

Answer 17

@Dhalsim ...bump the question

Answer 18

Opcode....did I mess up big time on this one

Answer 19

@cwrw238 ...help

Answer 20

@Dhalsim ...can you bump the question

Answer 21

I am sorry Dhalsim....I tried

Answer 22

I cant bump for aqnother 35 minutes. And thank you. ill figure it out i hope

Answer 23

@texaschic101 the profit is $15 per unit for the first product and $10 per unit for the second product. The profit is the result of selling price minus cost. Subtracting cost from profit doesn't really mean anything.

Answer 24

Also

x >=30
y >=20

Answer 25

I just thought taking the profit and subtracting the cost of making the item would result in how much you actually make

Answer 26

I caught my messing up of the inequality signs...I listed my mistake a few posts above

Answer 27

Cost was already subtracted from the sales price to produce profit. You can't subtract it again.

Answer 28

oh.....I see
but you would still make more from selling product 2 wouldn't you ?

Answer 29

so wouldn't you want to sell the least amount of product 1 and more of product 2

Answer 30

There are more test points involved than you think. You have to test all of them to be certain.

Answer 31

Is there a certain way to solve this ?

Answer 32

Because he is talking about graphing and shading

Answer 33

Yes, that's what it involves...figuring out the solution region.

Answer 34

I am so not good at that :(

Answer 35

It's not really that difficult.

Answer 36

We already know

x >=30
y >=20
3x + 5y <=340

Graphing that creates the region.

Answer 37

Graphing that should generate at least three possible test points

Answer 38

so is the slope -3/5 ?

Answer 39

That appears to be correct.

Answer 40

And the those two points are tested in the profit equation

P(x,y) = 10x + 15y

Answer 41

(80,20) appears to be the correct one.

Answer 42

oh...I was getting my numbers out of the cost equation

Answer 43

I suppose you didn't understand how those points were generated to begin with.

Answer 44

3x + 5y <= 340
3(80) + 5(20) <= 340
240 + 100 <= 340
yep...that one works
3x + 5y <= 340
3(30) + 5(50) <= 340
90 + 250 <= 340
yep..that works also

How did you get so smart.....I wish there was a pill that a person could take that would make them smart......why not, there is a pill for everything else

Answer 45

your points work in this inequality

Answer 46

Yeah, you're right, I thought I calculated them wrong.

Answer 47

Hero...you need to invent a smart pill

Answer 48

Nah, I think the movie limitless demonstrated why such a pill won't ever be created. People will just overdose on it and half the world's population would just get really sick or die.

Answer 49

your probably right....they would overdose trying to get too smart...

Answer 50

thanks Hero...your the best :)

Answer 51

The most competitive people would probably die because they would probably think that IQ is directly proportional to how many pills you consume.

Answer 52

lol.......they would overdose trying to be geniuses.....losing their common sense when it comes to how many pills one can take without overdosing

Answer 53

I am gonna go now hero....thanks again :)