Answer:
The company must use of of the Xavier's product in order to use the leftover stock to package 3 Zena's Product.
Step-by-step explanation:
The Xavier set contains one blue ink refill and one black ink refill.
The Yvonne set includes two blue ink refills, three black ink refills, and one red ink refill.
The Zena set includes four blue ink refills, five black ink refills, and one red ink refill.
Let the products be:
Xavier(x)
Yvonne(y)
Zena(z).
For the Blue Cartridge
Xavier Uses 1, Yvonne uses 2 and Zena uses 4.
1x+2y+4z
For the Black Cartridge
Xavier Uses 1, Yvonne uses 3 and Zena uses 5.
1x+3y+5z
For the Red Cartridge
Xavier Uses 0, Yvonne uses 4 and Zena uses 1.
0x+4y+1z
Inventory Left
Blue= 11 ink cartridge refills,
Black= 14 ink cartridge refills,
Red= 3 ink cartridge refills.
Therefore, in order to use all the cartridges left:
1x+2y+4z=11
x+3y+5z=14
4y+z=3
From equation 3
z=3-4y
Substitute into equations 1 and 2
1x+2y+4z=11
x+2y+4(3-4y)=11
x+2y+12-16y=11
x-14y=-1
x+3y+5z=14
x+3y+5(3-4y)=14
x+3y+15-20y=14
x-17y=-1
Solving the resulting equations
x-14y=-1
x-17y=-1
3y=0
y=0
Substituting y=0 into x-17y=-1
x=-1
Recall:
z=3-4y
z=3.
x=-1, y=0, z=3.
The company must use of of the Xavier's product in order to use the leftover stock to package 3 Zena's Product.
Note: You can use Gaussian Elimination Method to solve the system of linear equations.
and you're done.
