Question 70495: well for class we have to read a word problem and define variables i dont know how to do this ..here is the problem
Wanda, Xavier, and yolanda have a small business producing handmade shawls and afghans for the Mathematics Teachers Retirement Home. They spin the yarn, dye the yarn, and weave the cloth. A shawl requires one hour of spinning, one hour of dyeing, and one hour of weaving. An afghan requires 2 hours of spinning one hour of dyeing and four hours of weaving. They make a profit of $16 per shawl and $20 per afghan. Xavier does the spinning on his day off when he can spend at most eight hours spinning. Yolanda does the dyeing on her day off when she can spend up to six hours dyeing. Wanda does all of the weaving on Friday and Saturday when she has at most fourteen hours available. The trio would like to maximize their profit.
Answer by josmiceli(19441)   (Show Source):
You can put this solution on YOUR website! Let L = the number of shawLs made
Let N = the number of afghaNs made
The hours needed to make a shawl are
(S-1, D-1, W-1) 3 hours total for Spinning, Dying, Weaving
The hours needed to make an afghan are
(S-2, D-1, W-4) 7 hours total for Spinning, Dying, Weaving
For the spinning process,
 represents the hours needed to make
L shawLs and N afghaNs
 eight hours are available for spinning process
when L shawLs and N afghaNs are made
likewise,
 six hours are available for dying when L shawLs and N afghaNs are made
 fourteen hours are available for dying when L shawLs and N afghaNs are made
I next graph L versus N for each equation and see what makes sense
L is measured on the vertical axis, n on the horizontal
As I see from the graph, If N were > 3.5, the weaving process
would not get done at all, so
As I see from the graph, If L were > 6, the dying process
would not get done at all, so
The equation for profit is
The range of possible L and N are in the area enclosed by the
lines and the axes. An s,d,or w means not possible because there are
not enough hours to complete one of the 3 processes. Otherwise,
I note the profit.
(N,L)
(3,1)76.....(2,1)56....(1,1)36
(3,2)92.....(2,2)72....(1,2)52
(3,3)s,w....(2,3)88....(1,3)68
(3,4)s,d,w..(2,4)104...(1,4)84
(3,5)s,d,w..(2,5)s,d...(1,5)100
The maximum profit of $104 occurs when 2 afghans and 4 shawls
are made. Xavier spends  hours spinning. Yolande
spends  hours dyeing. Wanda spends 
hours weaving.
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