Intermediate Algebra -- Maximize profit when manufacturing clothes

[BrettJimison]

Homework Statement

Hello all,

Can someone help me figure this out?

"It takes cosmic stitching 2 hrs of cutting and 4 hrs of sewing to make a knit suit.
To make a worsted suit, it takes 4 hrs of cutting and 2 hrs of sewing. At most 20 hrs per day are available
for cutting and at most 16 hrs are available for sewing. The profit on a knit suit is $68 and the profit on a worsted suit is $62. How many of each kind should be made to maximize profit?"

Homework Equations

These are the eqn's/ inequalities I came up with:
Let c = cutting
Let s = sewing

c (less than or equal to) 20
s (less than or equal to)16

c+s (less than or equal to) 24 hrs

The Attempt at a Solution

I graphed c on the y-axis and s on the x-axis and found the two points of intersection of the function c=-s+24

they are (4,20) and (16,8).

Not sure what to do know (note I got to the answer by using logic, but the books answer has the answer in (x,y) form, which means that they somehow created a graph of knitted suits vs. worsted suits...

Can anyone help?

P.S You can be straight to the point, as embarrassing as it is, I tutor up through most of calc and physics.
Its been years since I have done these types of problems, and this one was presented to me at the tutoring center at which I work.

 

[BrettJimison]

One more function I left out: P(k,w)= 68k+62s where k = knit suits and w=worsted suits.
P(k,w) is the profit function

 

[Ray Vickson]

Homework Statement

Hello all,

Can someone help me figure this out?

"It takes cosmic stitching 2 hrs of cutting and 4 hrs of sewing to make a knit suit.
To make a worsted suit, it takes 4 hrs of cutting and 2 hrs of sewing. At most 20 hrs per day are available
for cutting and at most 16 hrs are available for sewing. The profit on a knit suit is $68 and the profit on a worsted suit is $62. How many of each kind should be made to maximize profit?"

Homework Equations

These are the eqn's/ inequalities I came up with:
Let c = cutting
Let s = sewing

c (less than or equal to) 20
s (less than or equal to)16

c+s (less than or equal to) 24 hrs

The Attempt at a Solution

I graphed c on the y-axis and s on the x-axis and found the two points of intersection of the function c=-s+24

they are (4,20) and (16,8).

Not sure what to do know (note I got to the answer by using logic, but the books answer has the answer in (x,y) form, which means that they somehow created a graph of knitted suits vs. worsted suits...

Can anyone help?

P.S You can be straight to the point, as embarrassing as it is, I tutor up through most of calc and physics.
Its been years since I have done these types of problems, and this one was presented to me at the tutoring center at which I work.

When I used to teach this stuff (in an Operations Research program) I would tell a student that one way to figure out what the appropriate variables are would be to imagine that you are the manager. What instructions would you need to tell your staff in order that they could go off and do their jobs? Just telling them to use so many hours of cutting and so many hours of sewing would be useless: they still would not know what to do! Use the sewing how? Use the cutting how? So, your variables do not "work".

Instead, if you tell them to make K knit suits and W worsted suits they could just go away and do it. For that reason those are appropriate variables in this problem.

Now, in terms of K = number of knit suits and W = number of worsted suits, what are: the total number of cutting hours and the total number of sewing hours used? What are the resulting restrictions due to sewing and cutting? What is the total profit?

I think you can take it from here.

 

[BrettJimison]

Ray, thanks for the response. I'll take it from there ;)