4. An electronics company produces transistors, resistors and computer chips. Ea

Question

4. An electronics company produces transistors, resistors and computer chips. Each transistors
requires 3 units of copper, 1 unit of zinc, and 2 units of glass. Each resistors requires 3, 2
and 1 units of the three materials, and each computer chips requires 2, 1, and 2 units of these
materials, respectively. How many of each product can be made with the following amount
of materials?
(a) 810 units of copper, 410 units of zinc, and 490 units of glass
(b) 765 units of copper, 385 units of zinc, and 470 units of glass
(c) 1010 units of copper, 500 units of zinc, and 610 units of glass

Explanation / Answer

Let x transistors, y resistor and z computer chips are produced.
units of copper required = 3x + 3y + 2z
units of zinc required = x + 2y + z
units of glass required= 2x + y + 2z

a.
3x + 3y + 2z = 810
x + 2y + z = 410
2x + y + 2z = 490

Solving,
x = 100, y = 110, z = 90

b.
3x + 3y + 2z = 765
x + 2y + z = 385
2x + y + 2z = 470

Solving,
x = 95, y = 100, z = 90

c.
3x + 3y + 2z = 1010
x + 2y + z = 500
2x + y + 2z = 610

Solving,
x = 140, y= 130, z = 100

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