Q7-15OQ The Goodparts Company produces a... [FREE SOLUTION]

Chapter 2: Q7-15OQ (page 162)

The Goodparts Company produces a component that is subsequently used in the aerospace industry. The component consists of three parts (A, B, and C) that are purchased from outside and cost 40, 35, and 15 cents per piece, respectively. Parts A and B are assembled first on assembly line 1, which produces 140 components per hour. Part C undergoes a drilling operation before being finally assembled with the output from assembly line 1. There are in total six drilling machines, but at present only three of them are operational. Each drilling machine drills part C at a rate of 50 parts per hour. In the final assembly, the output from assembly line 1 is assembled with the drilled part C. The final assembly line produces at a rate of 160 components per hour. At present, components are produced eight hours a day and five days a week. Management believes that if need arises, it can add a second shift of eight hours for the assembly lines. The cost of assembly labor is 30 cents per part for each assembly line; the cost of drilling labor is 15 cents per part. For drilling, the cost of electricity is one cent per part. The total overhead cost has been calculated as $1,200 per week. The depreciation cost for equipment has been calculated as $30 per week.
a. Draw a process flow diagram and determine the process capacity (number of components produced per week) of the entire process.
b. Suppose a second shift of eight hours is run for assembly line 1 and the same is done for the final assembly line. In addition, four of the six drilling machines are made operational. The drilling machines, however, operate for just eight hours a day. What is the new process capacity (number of components produced per week)? Which of the three operations limits the capacity?
c. Management decides to run a second shift of eight hours for assembly line 1 plus a second shift of only four hours for the final assembly line. Five of the six drilling machines operate for eight hours a day. What is the new capacity? Which of the three operations limits the capacity?
d. Determine the cost per unit output for questions (b) and (c).
e. The product is sold at $4.00 per unit. Assume that the cost of a drilling machine (fixed cost) is $30,000 and the company produces 8,000 units per week. Assume that four drilling machines are used for production. If the company had an option to buy the same part at $3.00 per unit, what would be the break-even number of units?

Short Answer

Expert verified

a. 6400 units per week

b. 8000 units per week, drill machine

c. 9600 units per week, last assembly line

d. 1.81, 1.64

e. 100840 units

Step by step solution

Understanding the process capacity

Process capacity is the capacity of humans or machines for production.

Obtaining formula for process capacity

$惭补肠丑颈苍别鈥塩补辫补肠颈迟测鈥� = 辞辫别谤补迟颈苍驳鈥塰辞耻谤蝉鈥� 脳辞辫别谤补迟颈苍驳鈥塺补迟别脳苍耻尘产别谤鈥塷蹿鈥尘补肠丑颈苍别蝉$

Making a flow diagram for the entire process

Step 4: Calculating the process capacity for the entire proces

$\begin{matrix} 颁补辫补肠颈迟测鈥塷蹿鈥碱蝉蝉别尘产濒测鈥塴颈苍别鈥� 1 = 140 鈥� u n i t s / h r 脳 8 鈥� h r / d a y 脳 5 鈥� d a y s / w e e k \\ = 5, 600 鈥� u n i t s / w e e k \end{matrix}$

$\begin{matrix} 颁补辫补肠颈迟鈥塷蹿鈥塪谤颈濒濒鈥尘补肠丑颈苍别蝉 = 3 鈥� d r i l l 鈥� m a c h i n e 脳 50 鈥� p a r t s / h r 脳 8 h r / d a y 脳 5 鈥� d a y s / w e e k \\ = 6, 000 鈥� u n i t s / w e e k \end{matrix}$

$\begin{matrix} 颁补辫补肠颈迟测鈥塷蹿鈥塮颈苍补濒鈥塧蝉蝉别尘产濒测鈥塴颈苍别 = 160 鈥� u n i t s / h r 脳 8 鈥� h r / d a y 脳 5 鈥� d a y s / w e e k \\ = 6, 400 鈥� u n i t s / w e e k \end{matrix}$

Finding the capacity of the entire process and limiting capacity

The capacity of the process is always the bottleneck process and the limiting capacity. In the above case, the assemblyline is the bottleneck process and the limiting capacity.

Step 5: Calculating new process capacity

$\begin{matrix} 颁补辫补肠颈迟测鈥塷蹿鈥塧蝉蝉别尘产濒测鈥塴颈苍别鈥�1 = 140 鈥� u n i t s / h r 脳 16 鈥� h r / d a y 脳 5 鈥� d a y s / w e e k \\ = 11, 200 鈥� u n i t s / w e e k \end{matrix}$

$\begin{matrix} 颁补辫补肠颈迟测鈥塷蹿鈥塪谤颈濒濒鈥尘补肠丑颈苍别蝉 = 4 d r i l l 鈥� m a c h i n e s 脳 50 鈥� p a r t s / h r 脳 8 鈥� h r / d a y 脳 5 鈥� d a y s / w e e k \\ = 8, 000 鈥� u n i t s / w e e k \end{matrix}$

$\begin{matrix} C a p a c i t y 鈥� o f 鈥� f i n a l 鈥� a s s e m b l y = 160 鈥� u n i t s / h r 脳 16 鈥� h r / d a y 脳 5 鈥� d a y s / w e e k \\ = 12, 800 鈥� u n i t s / w e e k \end{matrix}$

Analyzing which operation is limiting the capacity

The bottleneck is the capacity of the process and also the limiting capacity. In the case above,the capacity of the drill machine is the bottleneck.

Calculating new capacity for the changes made

c. $\begin{matrix} 颁补辫补肠颈迟测鈥塷蹿鈥塧蝉蝉别尘产濒测鈥塴颈苍别鈥�1 = 140 鈥� u n i t s / h r 脳 16 鈥� h r / d a y 脳 5 鈥� d a y s / w e e k \\ = 11, 200 鈥� u n i t s / w e e k \end{matrix}$

$\begin{matrix} 颁补辫补肠颈迟测鈥塷蹿鈥塪谤颈濒濒鈥尘补肠丑颈苍别 = 5 鈥� d r i l l 鈥� m a c h i n e s 脳 50 鈥� p a r t s / h r 脳 8 鈥� h r / d a y 脳 5 鈥� d a y s / w e e k \\ = 10, 000 鈥� u n i t s / w e e k \end{matrix}$

$\begin{matrix} 颁补辫补肠颈迟测鈥塷蹿鈥塮颈苍补濒鈥塧蝉蝉别尘产濒测 = 160 鈥� u n i t s / h r 脳 12 鈥� h r / d a y 脳 5 鈥� d a y s / w e e k \\ = 9, 600 鈥� u n i t s / w e e k \end{matrix}$

Analyzing the changed operation which is limiting the capacity

9,600 units per week is the capacity of the entire process, and the limiting capacity is the final assembly line.

Calculating the cost per unit output of b

d. Calculating the total cost per week when output is 8000

$\begin{matrix} 颁辞蝉迟鈥塷蹿鈥塸补谤迟鈥碱 \\ = 0.40 脳 8000 \\ = $ 3, 200 \end{matrix}$

$\begin{matrix} 颁辞蝉迟鈥塷蹿鈥塸补谤迟鈥塀 \\ = 0.35 脳 8000 \\ = $ 2, 800 \end{matrix}$

$\begin{matrix} 颁辞蝉迟鈥塷蹿鈥塸补谤迟鈥塁 \\ = 0.15 脳 8, 000 \\ = $ 1, 200 \end{matrix}$

$\begin{matrix} Electricity \\ = 0.01 脳 8, 000 \\ = $ 80 \end{matrix}$

$\begin{matrix} 尝补产辞谤鈥塩辞蝉迟鈥塷蹿鈥塧蝉蝉别尘产濒测鈥�1 \\ = 0.30 脳 8, 000 \\ = $ 2, 400 \end{matrix}$

$\begin{matrix} 尝补产辞谤鈥塩辞蝉迟鈥塷蹿鈥塮颈苍补濒鈥塧蝉蝉别尘产濒测 \\ = 0.30 脳 8, 000 \\ = $ 2, 400 \end{matrix}$

$\begin{matrix} 颁辞蝉迟鈥塷蹿鈥塪谤颈濒濒颈苍驳鈥塴补产辞谤 \\ = .15 脳 8000 \\ = $ 1200 \end{matrix}$

$\begin{matrix} 翱惫别谤丑别补诲鈥塩辞蝉迟 \\ = $ 1200 鈥� p e r 鈥� w e e k \end{matrix}$

$\begin{matrix} Depreciation \\ = $ 30 鈥� p e r 鈥� w e e k \end{matrix}$

$Total=$14,510$

$\begin{matrix} 颁辞蝉迟鈥塸别谤鈥塽苍颈迟 = \frac{罢辞迟补濒鈥塩辞蝉迟鈥塸别谤鈥墂别别办}{狈耻尘产别谤鈥塷蹿鈥塽苍颈迟蝉鈥塸谤辞诲耻别诲鈥塸别谤鈥墂别别办} \\ = \frac{$ 14, 510}{8, 000} \\ = $ 1.81 \end{matrix}$

Calculating the cost per unit output of c

_{Calculating total cost per week when output is 9600 units}

_{$\begin{matrix} 颁辞蝉迟鈥塷蹿鈥塸补谤迟鈥碱 \\ = 0.40 脳 9, 600 \\ = $ 3, 840 \end{matrix}$}

\begin{matrix} 颁辞蝉迟鈥塷蹿鈥塸补谤迟鈥塀 \\ = 0.35 脳 9, 600 \\ = $ 3, 360 \end{matrix}

$\begin{matrix} 颁辞蝉迟鈥塷蹿鈥塸补谤迟鈥塁 \\ = 0.15 脳 9, 600 \\ = $ 1, 440 \end{matrix}$

$\begin{matrix} 贰濒别肠迟谤颈肠颈迟测鈥塩辞蝉迟 \\ = 0.01 脳 9, 600 \\ = $ 96 \end{matrix}$

$\begin{matrix} 尝补产辞谤鈥塩辞蝉迟鈥塷蹿鈥塧蝉蝉别尘产濒测鈥�1 \\ = 0.30 脳 9, 600 \\ = $ 2, 880 \end{matrix}$

$\begin{matrix} 颁辞蝉迟鈥塷蹿鈥塪谤颈濒濒颈苍驳鈥塴补产辞谤 \\ = 0.30 脳 9, 600 \\ = $ 2, 880 \end{matrix}$

$\begin{matrix} 翱惫别谤丑别补诲鈥塩辞蝉迟 \\ = $ 1200 p e r 鈥� w e e k \end{matrix}$

$\begin{matrix} Depriciation \\ = $ 30 鈥� p e r 鈥� w e e k \end{matrix}$

$Total=$15,726$

$\begin{matrix} 颁辞蝉迟鈥塸别谤鈥塽苍颈迟 = \frac{罢辞迟补濒鈥塩辞蝉迟鈥塸别谤鈥墂别别办}{狈耻尘产别谤鈥塷蹿鈥塽苍颈迟蝉鈥塸谤辞诲耻肠别诲鈥塸别谤鈥墂别别办} \\ = \frac{$ 15, 726}{9, 600} \\ = $ 1.64 \end{matrix}$

Calculating the break-even number of units

e. Let the number of units to be produced by each option be $x$

The cost of buying the units is $3 per unit = $3 x$

When they manufacture, they incur a fixed cost of $120,000 and a cost per unit of $1.81 x$

Forming them into the equation

$\begin{matrix} 3 x = 120, 000 + 1.81 x \\ 3 x 鈭� 1.81 x = 120, 000 \\ 1.19 x = 120, 000 \\ x = \frac{120, 000}{1.19} \\ x = 100, 840 鈥� u n i t s \end{matrix}$

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TASK	Task Time (Seconds)	Immediate Predecessor
A	30	-
B	35	A
C	30	A
D	35	B
E	15	C
F	65	C
G	40	E, F
h	25	D, G

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Short Answer

Step by step solution

Understanding the process capacity

Obtaining formula for process capacity

Making a flow diagram for the entire process

Step 4: Calculating the process capacity for the entire proces

Finding the capacity of the entire process and limiting capacity

Analyzing which operation is limiting the capacity

Calculating new capacity for the changes made

Analyzing the changed operation which is limiting the capacity

Calculating the cost per unit output of b

Calculating the cost per unit output of c

Calculating the break-even number of units

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