# Assume that the production of 1 unit of magnesium requires 0.4 unitsof magnesium and 0.4 units of aluminum, and that the production of 1 unit of aiuminum requires 0.2 units of magnesium and 0.7 units of aluminumFind the production schedule that satisfies an external demand for 30 units of magnesium and 90 units of aluminum.X =

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Assume that the production of 1 unit of magnesium requires 0.4 units of magnesium and 0.4 units of aluminum, and that the production of 1 unit of aluminum requires 0.2 units of magnesium and 0.7 units of aluminum.

Find the production schedule that satisfies an external demand for 30 units of magnesium and 90 units of aluminum. help_outlineImage TranscriptioncloseAssume that the production of 1 unit of magnesium requires 0.4 units of magnesium and 0.4 units of aluminum, and that the production of 1 unit of aiuminum requires 0.2 units of magnesium and 0.7 units of aluminum Find the production schedule that satisfies an external demand for 30 units of magnesium and 90 units of aluminum. X = fullscreen
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Step 1

First construct a matrix A,

Step 2

By help of the matrix B find the production schedule matrix X, which is given by

X = (I – A)-1 * D

First find the matrix (I – A), then find its inve... help_outlineImage Transcriptionclose-0.2 0.4 0.2 1 0 I - A= 0 1 0.6 0.3 0.4 0.7 -0.4 (-A) 0.6 -0.2 3 2 -0.4 0.3 4 6 270 3.30 2.90 30 3 2 (1-A) D= 4-30 6.90 4 6 90 660 270 X(I-A) D 660 fullscreen

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