Question

In: Advanced Math

A company manufactures three types of luggage: economy, standard, and deluxe.

A company manufactures three types of luggage: economy, standard, and deluxe. The
company produces 1000 pieces each month. The cost for making each type of luggage is
$20 for the economy model, $30 for the standard model, and $40 for the deluxe model.
The manufacturer has a budget of $25,700. Each economy piece requires 6 hours of
labor, the standard model requires 8 hours of labor and the deluxe requires 12 hours of
labor. The manufacturer has a total of 7400 hours of labor available each month. If the
manufacturer sells all of the luggage produced, exhausts his entire budget and uses all
available hours of labor, how many pieces of each can be produced?

a) Write the system of equations for this information. Identify variables.

b) Write the augmented matrix for this information.

c) Solve using the Gauss-Jordan elimination method. Label each answer.

Solutions

Expert Solution

x=economy

y=standard

z=deluxe

The company produces 1000 pieces each month

The cost for making each type of luggage is $20 for the economy model, $30 for the standard model, and $40 for the deluxe model. The manufacturer has a budget of $25,700.

Each economy piece requires 6 hours of labor, the standard model requires 8 hours of labor and the deluxe requires 12 hours of labor. The manufacturer has a total of 7400 hours of labor available each month.

total 3 equations are

system Ax=b is

augmented matrix is

solution is

560=economy

310=standard

130=deluxe

Colby Messinger answered 1 year ago

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