Question 231252
Let {{{a}}} = number of batches of cookies she could make
Let {{{b}}} = number of batches of cupcakes she could make
given:
{{{20 <= 15a + 12b <= 360}}}
{{{15a >= 3*12b}}}
{{{15a >= 36b}}}
-----------------
{{{15a + 12b >= 20}}}
{{{15a >= 20 - 12b}}}
(1) {{{a >= -(4/5)*b + 4/3}}}
and
{{{15a + 12b <= 360}}}
{{{15a <= 360 - 12b}}}
(2) {{{a <= -(4/5)*b + 24}}}
and
(3) {{{a >= (12/5)*b}}}
If I plot a on vertical, b on horizontal for these 3 equations, I get
{{{ graph( 600,600,-10,50,-10,50,-(4/5)*x + 4/3,-(4/5)*x + 24,(12/5)*x )}}}
It looks like the solution is the small triangular
region bounded by the 3 lines and the a-axis
If I try {{{a=18}}} and {{{b=6}}}, then
{{{20 <= 15a + 12b <= 360}}}
{{{20 <= 15*18 + 12*6 <= 360}}}
{{{20 <= 270 + 72 <= 360}}}
{{{20 <= 342 <= 360}}}
OK, and
{{{15a >= 36b}}}
{{{5a >= 12b}}}
{{{5*18 >= 12*6}}}
{{{90 >= 72}}}
Hope I got it right- I think so