The Acme Class Ring Company Designs and sells two type of rings: the
VIP and the SST. They can Prduce up to 24 rings each day using up to
60 total man- hours of labor. it takes 3 man hours to make one VIP
ring and 2 man hours to make one SST ring. How many of each type of
ring should be made daily to maximize the company's profit, if the
profit on a VIP ring is $30. and on a SST ring is $40.

let V be the number of vip ring and S the number of SST

S+V<=24                          
     BY ISOLATING S   S<=24-V
S*2 man hours +V* 3 man hours <=60man hours    
     BY ISOLATING S   S<=20-V

since v is always positive if S<=20-V it's always <=24-V

now we need to find the max of the following equ

V*$30+S*$40

By replacing S by 20-V we get

V*$30+(20-V)*$40=800-10V

again since V cannot be negative the max if when V = 0

So there is no solution to this problem????

The answer is when V=0.  If you plug the value of V into the other
equations, your answer for S is S=24.  There are some slight errors in
the calculations of the commentor above, but the answer is correct. 
Think about it logically, the SST requires less time to make and
generates more profit per ring.  Making any of the VIP would take more
time and generate less money.  Usually these types of questions are
arranged a little differently (with the item taking more time
generating more profit and vice versa) which makes me suspect that you
have a typo, but as written, your answer is 24 SST and 0 VIT.

Well, if they can make only 24 rings a day, shouldn't they only make SST's :)?
They only need 48 man-hours to accomplish this, leaving 12 man-hours
to go home, or they can make 4 VIP rings in the remaining time.

If it took longer to make (or the profit was less on) the SST than the
VIP, then the equation might have a bit more merit, don't you think?

This is a free comment.