PP.51 A small manufacturer of specialty welding equipment has developed a **chase** production plan for the next four quarters, as seen below:

**Supply/Demand Info**

**Pre-Q1**

**Q1**

**Q2**

**Q3**

**Q4**

Forecast (demand)

3,360

3,840

4,440

4,080

Regular production

3,360

3,840

4,440

4,080

Subcontract production

Ending inventory

Hired employees

4

5

Fired employees

2

3

Total employees

30

28

32

37

34

The table below shows additional relevant information:

**Capacity Information & Cost Variables**

Production rate (units/employee/quarter)

120

Subcontractor capacity (units/quarter)

510

Regular production cost/unit

$79

Holding cost/unit/quarter

$14

Hiring cost/employee

$860

Firing cost/employee

$2,400

Subcontract cost/unit

$117

What is the **overall total cost** for this production plan? (Display your answer to the nearest **whole number**.)

To calculate the **overall total cost** for the given production plan, we need to account for the following costs:

1. **Regular production cost** for each quarter.
2. **Holding cost** for any ending inventory.
3. **Hiring cost** for each quarter.
4. **Firing cost** for each quarter.
5. **Subcontracting cost**, if subcontracting is used.

### Step-by-step calculation:

#### 1. **Regular Production Cost**:
The regular production for each quarter is given, and the cost per unit is \$79. The total regular production cost for each quarter is calculated as:

\[
\text{Regular Production Cost} = \text{Regular Production Units} \times \text{Cost per Unit}
\]

- Q1: $3,360 \times 79 = 265,440$
- Q2: $3,840 \times 79 = 303,360$
- Q3: $4,440 \times 79 = 350,760$
- Q4: $4,080 \times 79 = 322,320$

**Total Regular Production Cost**:  
$265,440 + 303,360 + 350,760 + 322,320 = 1,241,880$

#### 2. **Holding Cost**:
Since no ending inventory is mentioned, there is **no holding cost**.

#### 3. **Hiring Cost**:
The number of employees hired in each quarter is given. The hiring cost per employee is \$860.

- Q1: $4 \times 860 = 3,440$
- Q2: $5 \times 860 = 4,300$
- Q3: No hiring, so cost = 0
- Q4: No hiring, so cost = 0

**Total Hiring Cost**:  
$3,440 + 4,300 = 7,740$

#### 4. **Firing Cost**:
The number of employees fired in each quarter is given. The firing cost per employee is \$2,400.

- Q1: $2 \times 2,400 = 4,800$
- Q2: $3 \times 2,400 = 7,200$
- Q3: No firing, so cost = 0
- Q4: No firing, so cost = 0

**Total Firing Cost**:  
$4,800 + 7,200 = 12,000$

#### 5. **Subcontracting Cost**:
Since there is no subcontracted production mentioned, **there is no subcontracting cost**.

### **Overall Total Cost**:

Now, summing up all the costs:

\[
\text{Overall Total Cost} = \text{Regular Production Cost} + \text{Hiring Cost} + \text{Firing Cost}
\]

\[
\text{Overall Total Cost} = 1,241,880 + 7,740 + 12,000 = 1,261,620
\]

Thus, the **overall total cost** for this production plan is **\$1,261,620**.

Would you like further details or explanations on any part? Here are some related questions for deeper exploration:

1. What would happen to the total cost if ending inventory were factored in?
2. How would the total cost change if subcontracting were used in one of the quarters?
3. What is the impact of varying hiring and firing costs on the total production cost?
4. How would an increase in production rate per employee affect the overall cost?
5. What strategies could be used to reduce the overall cost in future quarters?

**Tip:** Holding costs can sometimes accumulate if there's excess production, so managing inventory efficiently is crucial.

A small manufacturer of specialty welding equipment has developed a chase production plan for the next four quarters. Given the supply/demand information and cost variables, calculate the overall total cost of the production plan to the nearest whole number.

Discover how to calculate the overall total cost for a small manufacturer’s chase production plan across four quarters. This problem involves cost analysis of regular production, hiring, and firing using key production planning concepts. Ideal for students in undergraduate operations management or business programs.

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