Question

a clothing manufacturer makes coats, shirts and slacks. The time required for The Cutting, sewing, and packaging on each item is shown in the table. How many of each should be made to use all available labor hours?​

Answer 1

Answer:

If we let c, s, p represent quantities of coats, shirts, pants, respectively, then the total number of minutes required for cutting, sewing, and packaging can be expressed by ...

  20c +15s +10p = 7200

  60c +30s +24p = 17520

  5c +12s +6p = 4080

Answer 2

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Answer:

  120 coats, 200 shirts, 180 slacks

Step-by-step explanation:

If we let c, s, p represent quantities of coats, shirts, pants, respectively, then the total number of minutes required for cutting, sewing, and packaging can be expressed by ...

  20c +15s +10p = 7200

  60c +30s +24p = 17520

  5c +12s +6p = 4080

These equations can be written in "augmented matrix" form and submitted to your friendly local matrix solver (online or on your calculator). You would ask for "reduced row-echelon form". The calculator function that accomplishes this is often called RREF. The matrix and result are ...

  $\left[\begin{array}{ccc|c}20&15&10&7200\\60&30&24&17520\\5&12&6&4080\end{array}\right]\rightarrow \left[\begin{array}{ccc|c}1&0&0&120\\0&1&0&200\\0&0&1&180\end{array}\right]$

This means production should be of ...

  120 coats, 200 shirts, 180 slacks