Question 70495
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,
{{{L + 2N}}} represents the hours needed to make 
L shawLs and N afghaNs
{{{L + 2N <= 8}}} eight hours are available for spinning process
when L shawLs and N afghaNs are made
likewise,
{{{L + N <= 6}}} six hours are available for dying when L shawLs and N afghaNs are made
{{{L + 4N <= 14}}} 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
{{{ graph( 400, 400, -4, 10, -4, 20, 8-2x, 6-x, 14-4x ) }}}
As I see from the graph, If N were > 3.5, the weaving process 
would not get done at all, so
{{{N < 3.5}}}
As I see from the graph, If L were > 6, the dying process
would not get done at all, so
{{{L < 6}}}
The equation for profit is 
{{{16L + 20N = P}}}
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 {{{L+2N = 8}}}hours spinning. Yolande
spends {{{L+N = 6}}}hours dyeing. Wanda spends {{{L+4N = 12}}}
hours weaving.