Chapter 14, Problem 44P

Kitchen Magician, Inc. has assembled the following data pertaining to its two most popular products.

Past experience has shown that the fixed manufacturing overhead component included in the cost per machine hour averages $10. Kitchen Magician’s management has a policy of filling all sales orders, even if it means purchasing units from outside suppliers.

Required:

1. 1. If 50,000 machine hours are available, and management desires to follow an optimal strategy, how many units of each product should the firm manufacture? How many units of each product should be purchased?
2. 2. With all other things constant, if management is able to reduce the direct material for an electric mixer to $6 per unit, how many units of each product should be manufactured? Purchased?
3. 3. Build a spreadsheet: Construct an Excel spreadsheet to solve requirement (1) above. Show how the solution will change if the following information changes: the unit cost if purchased from an outside supplier is $22 for the blender and $40 for the electric mixer.

To determine

Calculate the number units to be purchased.

Explanation of Solution

Decision making process: Decision making process requires an understanding of a grasp of illegal issues, quantitative and qualitative information, and an ability to discern fact from opinion and sensitivity to ethical concerns.

Calculate the number units to be purchased:

Particulars	Amount
Machine hours available	50,000
Machine hours needed to manufacture 20,000 blenders	20,000
Remaining machine hours	30,000
Number of mixers to be produced	15,000

Table (1)

Conclusion:

• Manufacture 20,000 blenders.
• Manufacture 15,000 mixers.
• Purchase 13,000 mixers $(28,000-15,000)$ .

Working note:

(1)Calculate the machine hours required per unit:

Particulars	Blender	Electric Mixer
Unit cost if purchased from an outside supplier	$20	$38
Incremental unit cost if manufactured:
Direct material	$6	$11
Direct labor	$4	$9
Variable overhead	(5) $6	(6) $ $12
Total	$16	$32
Unit cost savings if manufactured	$ 4	$6
Machine hours required per unit	(3) $1	(4) $2
Cost savings per machine hour if manufactured
$\frac{\text{\$4}}{\text{1hour}}$	$4
$\frac{\text{\$6}}{\text{2hour}}$		$3

Table (2)

(2)Calculate the number of mixes to be produced:

$\begin{array}{c}\begin{array}{l}\text{Number}\text{of}\text{mixers}\\ \text{to}\text{be}\text{produced}\end{array}\}\text{=}\frac{\text{Remaining}\text{machine}\text{hours}}{\text{Machine}\text{hours}\text{required}\text{per}\text{unit}}\\ \text{=}\frac{\text{30,000}\text{hours}}{\text{2}\text{hours}\text{(1)}}\\ \text{=}\text{15,000}\end{array}$

(3)Calculate the machine hours required per unit for blender:

$\begin{array}{c}\text{Machine}\text{hours}\text{required}\text{per}\text{unit}\text{=}\frac{\text{Manufacturing}\text{cost}\text{of}\text{product}\text{blender}}{\text{Manufacturing}\text{overhead}\text{per}\text{machine}\text{hour}}\\ \text{=}\frac{\text{\$16}}{\text{\$16}}\\ \text{=\$1}\end{array}$

(4)Calculate the machine hours required per unit for electric mixer:

$\begin{array}{c}\text{Machine}\text{hours}\text{required}\text{per}\text{unit}\text{=}\frac{\text{Manufacturing}\text{cost}\text{of}\text{product}\text{electric}\text{mixer}}{\text{Manufacturing}\text{overhead}\text{per}\text{machine}\text{hour}}\\ \text{=}\frac{\text{\$32}}{\text{\$16}}\\ \text{=\$2}\end{array}$

(5)Calculate variable overhead for blender:

$\begin{array}{c}\text{Variable}\text{overhead}\text{=}\left(\begin{array}{l}\text{Manufacturing}\text{cost}\text{of}\text{product}\text{blender}-\\ \text{Cost}\text{per}\text{machine}\text{hour}\text{on}\text{average}\end{array}\right)\\ \text{=}\text{\$16}-\text{\$10}\\ \text{=\$6}\end{array}$

(6)Calculate variable overhead for electric mixer:

$\begin{array}{c}\text{Variable}\text{overhead}\text{=}\left[\begin{array}{l}\text{Manufacturing}\text{cost}\text{of}\text{product}\text{electric}\text{mixer}-\\ \left(\begin{array}{l}\text{Machine}\text{hours}\text{required}\text{per}\text{unit}\text{×}\\ \text{Cost}\text{per}\text{machine}\text{hour}\text{on}\text{average}\end{array}\right)\end{array}\right]\\ \text{=}\left[\text{\$32}-\left(\begin{array}{l}\text{2}\text{hour×}\\ \text{\$10}\end{array}\right)\right]\\ \text{=\$32}-\text{\$20}\\ \text{=\$12}\end{array}$

To determine

Calculate the number of units of each product that must be manufactured and purchased, if management is able to reduce the direct material for an electric mixer to $6 per unit while other things remaining constant.

Explanation of Solution

If the company’s management team can cut the direct material cost per mixer to $6 ($5 less than previously presumed), then the cost savings from manufacturing a mixer are $11 per unit ($6 savings calculated in requirement (1) including $5 reduction in material cost):

Particulars	Blender	Electric Mixer
New unit cost savings if manufactured	$ 4.00	$11.00
Machine hours required per unit	1 MH	2 MH
Cost savings per machine hour if manufactured
$\frac{\text{\$4}}{\text{1hour}}$	$ 4.00
$\frac{\text{\$11}}{\text{2hour}}$		$ 5.50

Table (3)

Therefore, devote all 50,000 hours to the production of 25,000 mixers.

Conclusion:

• Manufacture:  25,000 mixers $\left(\frac{\text{50,000}\text{hours}}{\text{2}\text{MH}\text{per}\text{unit}}\right)$ .
• Purchase:  3,000 mixers $(28,000-25,000)$ .
• Purchase:  20,000 blenders.

To determine

Build a spreadsheet to solve the requirement 1 and show the manner in which the solution will change if the unit cost from an outside supplier is $22 for the blender and $40 for the electric mixer.

Explanation of Solution

Construct spreadsheet:

Figure (1)

Working note:

Figure (2)