Question

the production supervisor at a particular office products company finds that it takes 4 hours to manufacture a particular office chair and 8 hours to manufacture a computer desk. a total of 3200 hours is available to produce office chairs and desks of this style. the linear equation that models this situation is 4x + 8y = 3200, where x represents the number of chairs produced and y the number of desks manufactured.
a. complete the ordered pair solution (0, ) of this equation. describe the manufacturing situation that corresponds to this solution.
the ordered pair is (0, )

Explanation:

Step1: Substitute \(x = 0\) into the equation \(4x+8y = 3200\)

Substitute \(x = 0\) into the linear equation \(4x + 8y=3200\). We get \(4\times0+8y=3200\), which simplifies to \(8y = 3200\).

Step2: Solve for \(y\)

To solve for \(y\), divide both sides of the equation \(8y = 3200\) by \(8\). Using the formula \(y=\frac{3200}{8}\).

Answer:

\(y = 400\). The ordered pair is \((0,400)\). This means that if no chairs (\(x = 0\)) are produced, then \(400\) desks (\(y = 400\)) can be manufactured, since \(4\times0+8\times400=0 + 3200=3200\) hours (which uses up all the available production hours).