Systems of Equations and Matrix Equations

Labor and material costs for manufacturing two guitar models are given in the table:

Guitar Model Labor Cost Material Cost

A $30 $20

B $40 $30

A. If a total of $3,000 a week is allowed for labor and material, how many of each model should be produced each week to use exactly each of the allocations of the $3,000 indicated in the following table?

Weekly Allocation

1 2 3

Labor $1,800 $1,750 $1,720

Material $1,200 $1,250 $1,280

B. Is it possible to use an allocation of $1,600 for labor and $1,400 for material? Explain your reasoning.

C. Explain, in your own words, why solving a matrix equation is a better method to solve this type of problem than Gauss Jordan elimination.