Questions: 2. A manager is trying to decide whether to rent a piece of equipment or buy the piece of equipment. To rent the piece of equipment, the costs would involve a flat fee of 50,000 as well as 6 per unit produced on the machine. If the manager was to buy the equipment outright, the cost would be 110,000. A. Develop the linear equations for renting versus buying the equipment. Cost to rent = CTR cost to buy = CTB CTR = 50,000+6x CTB = 110,000 X= units produced Renting: CTR=50,000+6x CTB=110,000 B. If current production volume is expected to be 13,000 units, should the manager rent or buy the

2. A manager is trying to decide whether to rent a piece of equipment or buy the piece of equipment. To rent the piece of equipment, the costs would involve a flat fee of 50,000 as well as 6 per unit produced on the machine. If the manager was to buy the equipment outright, the cost would be 110,000.
A. Develop the linear equations for renting versus buying the equipment.

Cost to rent = CTR cost to buy = CTB

CTR = 50,000+6x
CTB = 110,000
X= units produced

Renting:
CTR=50,000+6x
CTB=110,000
B. If current production volume is expected to be 13,000 units, should the manager rent or buy the

Transcript text: 2. A manager is trying to decide whether to rent a piece of equipment or buy the piece of equipment. To rent the piece of equipment, the costs would involve a flat fee of $\$ 50,000$ as well as $\$ 6$ per unit produced on the machine. If the manager was to buy the equipment outright, the cost would be $\$ 110,000$. A. Develop the linear equations for renting versus buying the equipment. Cost to rent $=$ CTR cost to buy $=$ CTB \[ \begin{aligned} \mathrm{CTR} & =50,000+6 \mathrm{x} \\ \mathrm{CTB} & =110,000 \end{aligned} \] \[ \mathrm{X}=\text { units produced } \] Renting: \[ \mathrm{CTR}=50,000+6 \mathrm{x} \] \[ \mathrm{CTB}=110,000 \] B. If current production volume is expected to be 13,000 units, should the manager rent or buy the

Solution

Solution Steps

To determine whether the manager should rent or buy the equipment, we need to compare the total costs for both options at the given production volume of 13,000 units. We will calculate the total cost for renting and the total cost for buying, and then compare the two.

Step 1: Define the Cost Equations

To determine the cost of renting and buying the equipment, we start with the given cost equations:

Cost to rent: $ \text{CTR} = 50000 + 6x $
Cost to buy: $ \text{CTB} = 110000 $

where $ x $ is the number of units produced.

Step 2: Calculate the Total Cost for Renting

Given the production volume $ x = 13000 $ units, we substitute $ x $ into the cost equation for renting: \[ \text{CTR} = 50000 + 6 \times 13000 \] \[ \text{CTR} = 50000 + 78000 \] \[ \text{CTR} = 128000 \]

Step 3: Compare the Costs

We compare the total cost to rent ($ \text{CTR} = 128000 $) with the total cost to buy ($ \text{CTB} = 110000 $):

\[ \text{CTR} = 128000 \] \[ \text{CTB} = 110000 \]

Since $ 128000 > 110000 $, the cost to rent is higher than the cost to buy.