Question

Set up a system of equations and then solve using a calculator.

A manufacturer of portable tools has three sets, Basic, Homeowner, and Pro, which must be painted, assembled, and packaged for shipping. The following table gives the number of hours required for each operation for each set.



Basic Homeowner Pro

Painting 1 1.7 2.9

Assembly 0.7 1.3 1.7

Packaging 0.8 0.9 1.4











If the manufacturer has 94.7 hours for painting per day, 63.1 hours for assembly per day, and 54.6 hours for packaging per day. How many sets of each type can be produced each day?



The manufacturer can produce _____ Basic sets, _____ Homeowner sets and_____ Pro sets per day.

Answer 1

Let \( x, y, \) and \( z \) represent the number of Basic, Homeowner, and Pro sets produced per day, respectively.

The system of equations based on the given information is:

\[ \begin{align*}
1x + 1.7y + 2.9z &= 94.7 \quad \text{(Painting)} \\
0.7x + 1.3y + 1.7z &= 63.1 \quad \text{(Assembly)} \\
0.8x + 0.9y + 1.4z &= 54.6 \quad \text{(Packaging)}
\end{align*} \]

Now, you can use a calculator or a tool like a matrix solver to find the values of \( x, y, \) and \( z \) that satisfy this system of equations. The solution will give you the number of Basic, Homeowner, and Pro sets that can be produced each day.