Question

A sporting good store receives a shipment of 124 golf bags. The shipment includes 2 types of bags, full-size and collapsible. The full-size bags cost $38.50 each. The collapsible bags cost $22.50 each. The bill for the shipment is $3430. How many of each type of golf bag are in the shipment? I need to define variables and write equations. I already have variables so how do I find the constraints?

Answer 1

Let

f = # of full-size bags
c = # of collapsible bags

"A sporting good store receives a shipment of 124 golf bags" which means

f+c = 124

"The full-size bags cost $38.50 each. The collapsible bags cost $22.50 each. The bill for the shipment is $3430" telling us

38.50f + 22.50c = 3430

Answer 2

So you have these two equations

f+c = 124
38.50f + 22.50c = 3430

do you know how to solve from here?

Answer 3

not really

Answer 4

Solve f+c = 124 for one of the variables

I'll pick c

f+c = 124

c = 124-f

Answer 5

Then you plug c = 124-f into the second equation


38.50f + 22.50c = 3430

38.50f + 22.50(124-f) = 3430

now solve for f

Answer 6

ok....thanks a lot!

Answer 7

once you find f, you can find c by plugging it into c = 124-f

Answer 8

I'm lost on how to solve for f...

Answer 9

I'll get you started


38.50f + 22.50(124-f) = 3430

38.50f + 22.50(124)+22.50(-f) = 3430

38.50f + 2790 - 22.50f = 3430

16f + 2790 = 3430

f = ??

Answer 10

is it like this: 38.50f = 22.50(124-f)=3430?

Answer 11

Oh, I see you wrote that

Answer 12

I got my x and y number, how would I graph this? x is 40, y is 84

Answer 13

what do you mean?

Answer 14

I need more constraints and I am trying to find the feasible region

Answer 15

when you solve 16f + 2790 = 3430, you get

16f + 2790 = 3430

16f = 3430-2790

16f = 640

f = 640/16

f = 40

Answer 16

Then you use this to find c

c = 124 - f

c = 124 - 40

c = 84

Answer 17

I don't see why you need to add constraints

Answer 18

Well, my objective function was 38.50x +22.50y=3430 and I am supposed to write restraints and find the feasible regions to graph it.

Answer 19

did you see how I got f = 40 and c = 84?

those values mean that we have 40 full-size bags and 84 collapsible bags

Answer 20

yes but how would I graph this to find the feasible region

Answer 21

check:

40+84 = 124

38.50*40 + 22.50*84 = 3430

so each works out

Answer 22

are you sure it doesn't say "up to 124 bags"? or anything like that?

Answer 23

No I wrote the problem exactly as it says. I think I got it. I graphed a line for 124 and the 84 and 40 were on the line.

Answer 24

honestly I'd just forget about the constraints and end the problem with saying "40 full-size bags and 84 collapsible bags"

this is because constraints are usually for optimization problems

Answer 25

I'd love to but I had to list the constraints and graph them and write a complete sentence about this problem. Love the common core.... I couldn't have done the problem without your help with the objective function, so thank you very much:)

Answer 26

I'm new to Open Study, how to I give you a vote? other than just "best response?"

Answer 27

hmm I see. I'm not familiar with the common core, but it sounds a bit frustrating. you click "best response" next to the person who you want to give a medal to

Answer 28

i don't mind really, so either way is fine

Answer 29

Ok, well, I did click, so I do really appreciate your help tonight:)

Answer 30

you're welcome