Q52. - Algebra 2

Question

How do linear equations apply to business?

 

Include the following in your answer:

• the fixed cost and the variable cost in the equation $\mathbf{y}=\mathbf{5400}+\mathbf{1}.\mathbf{37}\mathbf{x}$, where $\mathbf{y}$ is the cost for a company to produce $\mathbf{x}$ units of its product, and
• the cost for the company to produce 1000 units of its product.

Step-by-Step Solution

Answer

In business, linear equations can be used to model the cost for a company to produce some units of its product. Such a cost can be of two types; fixed cost, which is independent of the number of units of the product produced and variable cost, which depends on the number of units of the product produced by the company.

• The fixed cost is $5400$ units and the variable cost is $1.37x$ units.
• The cost for the company to produce 1000 units of its product is 6770 units.

Step 1 – State the concept

In business, linear equations can be used to model the cost for a company to produce some units of its product. Such a cost can be of two types; fixed cost, which is independent of the number of units of the product produced and variable cost, which depends on the number of units of the product produced by the company.

Step 2 – List the given data

The given equation modeling the cost for a company is given as $y=5400+1.37x$, where $y$ is the cost for the company to produce $x$ units of its product.

Step 3 – Determine the fixed and variable cost

The cost for the company is modeled by the equation, $y=5400+1.37x$.

Notice that this cost can be divided into two parts, $5400$ and $1.37x$. Clearly, $5400$ does not depend on the number of units of the product, $x$ and is thus the fixed cost. On the other hand, $1.37x$ depends on $x$ very obviously and thus is the variable cost.

Step 4 – Compute the required cost

Put $x=1000$ in $y=5400+1.37x$ to get,

$\begin{array}{l}y=5400+1.37\left(1000\right)\\ =5400+1370\\ =6770\end{array}$

This implies that the cost for the company to produce 1000 units of its product is 6770 units.