Question 149684
Tim works at a bakery and can prepare a birthday cake in 4 hours or less. It takes him 5 hours or less to prepare a wedding cake. If Tim works a 40-hour week , and if he must bake more birthday cakes than wedding cakes, what would the graph look like of the number of each type of cake time can bake per week. 
:
Let x = no. of b. cakes
Let y = no. of w. cakes
:
b.cake hrs + w.cake hrs = 40 hrs
:
4x + 5y = 40
5y = 40 - 4x
y = {{{40/5}}} - {{{4/5}}}x
y = 8 - .8x
:
Plot this from x=0 to x=10
Two points could be 
x = 5; y = 8 - .8(5); y = 4
and
x = 10; y = 8 -.8(10); y = 0 
:
Should look like this
{{{ graph( 300, 200, -4, 12, -4, 12, 8-.8x) }}} 
Now it said he has to make more b. cakes (x) than w.cakes (y)
another graph for this;
y < x (green)
:
now the graph looks like this:
{{{ graph( 300, 200, -4, 12, -4, 12, 8-.8x, x) }}} 
The area of feasibility would be bounded by:
 at or below the purple line
 to the right of the green line
;
did this make sense to you?