Question 1030008
Let {{{A}}} be the number of compact kits, {{{B}}} standard kits, {{{C}}} deluxe kits.
,
,
A(20,8,1)+B(40,20,2)+C(50,28,4)=(2900,1440,160)
,
,
{{{20A+40B+50C=2900}}}
1.{{{2A+4B+5C=290}}}
.
.
{{{8A+20B+28C=1440}}}
2.{{{2A+5B+7C=360}}}
.
.
3.{{{A+2B+4C=160}}}
In matrix form,
{{{(matrix(3,3,
2,4,5,
2,5,7,
1,2,4))*(matrix(3,1,A,B,C))=(matrix(3,1,290,360,160))}}}
.
.
.
Using Cramer's rule,
{{{X=(matrix(3,3,
2,4,5,
2,5,7,
1,2,4))}}}
{{{abs(X)=3}}}
.
.
{{{X[A]=(matrix(3,3,
290,4,5,
360,5,7,
160,2,4))}}}
{{{abs(X[A])=60}}}
.
.
{{{X[B]=(matrix(3,3,
2,290,5,
2,360,7,
1,160,4))}}}
{{{abs(X[B])=150}}}
.
.
{{{X[C]=(matrix(3,3,
2,4,290,
2,5,360,
1,2,160))}}}
{{{abs(X[C])=30}}}
.
.
{{{A=abs(X[A])/abs(A)=60/3=20}}}
.
.
{{{B=abs(X[B])/abs(A)=150/3=50}}}
.
.
{{{C=abs(X[C])/abs(A)=30/3=10}}}
.
.