Question

The Walton Toy Company manufactures a line of dolls and a sewing kit. Demand for the company’s products is increasing, and management requests assistance from you in determining an economical sales and production mix for the coming year. The company has provided the following data: Product Demand Next year (units) Selling Price per Unit Direct Materials Direct Labor Debbie 72,000 $ 18.00 $ 4.90 $ 4.05 Trish 64,000 $ 6.50 $ 1.80 $ 1.89 Sarah 57,000 $ 30.00 $ 9.74 $ 6.75 Mike 40,000 $ 15.00 $ 4.20 $ 4.95 Sewing kit 347,000 $ 10.20 $ 5.40 $ 1.44 The following additional information is available: The company’s plant has a capacity of 155,110 direct labor-hours per year on a single-shift basis. The company’s present employees and equipment can produce all five products. The direct labor rate of $9 per hour is expected to remain unchanged during the coming year. Fixed manufacturing costs total $605,000 per year. Variable overhead costs are $5 per direct labor-hour. All of the company’s nonmanufacturing costs are fixed. The company’s finished goods inventory is negligible and can be ignored. Required: 1. How many direct labor hours are used to manufacture one unit of each of the company’s five products? 2. How much variable overhead cost is incurred to manufacture one unit of each of the company’s five products? 3. What is the contribution margin per direct labor-hour for each of the company’s five products? 4. Assuming that direct labor-hours is the company’s constraining resource, what is the highest total contribution margin that the company can earn if it makes optimal use of its constrained resource? 5. Assuming that the company has made optimal use of its 155,110 direct labor-hours, what is the highest direct labor rate per hour that Walton Toy Company would be willing to pay for additional capacity (that is, for added direct labor time)?

Answer 1

Solution:

Part 1 --- Direct Labor Hours per unit

	Debbie	Trish	Sarah	Mike	Sewing Kit
Direct Labor Cost per unit (A)	$4.05	$1.89	$6.75	$4.95	$1.44
Direct Labor Rate Per Unit (B)	$9.00	$9.00	$9.00	$9.00	$9.00
Direct Labor Hours Per Unit (A/B)	0.45	0.21	0.75	0.55	0.16

Part 2 – Variable Overhead Per Unit

	Debbie	Trish	Sarah	Mike	Sewing Kit
Direct Labor Hours Per Unit (As calculated in Part 1) (A)	0.45	0.21	0.75	0.55	0.16
Variable Overhead Cost per direct labor hour (B)	$5.00	$5.00	$5.00	$5.00	$5.00
Variable Overhead Per Unit (A*B)	$2.25	$1.05	$3.75	$2.75	$0.80

Part 3 – Contribution Margin Per DLH

Product	Selling Price Per Unit	Direct materials per unit	Direct Labor per unit	Variable Overhead Per Unit (Refer Part 2)	Total Variable Cost per unit	Contribution margin per unit	Direct Labor Hours Needed Per Unit (refer part 1)	Contribution Margin per DLH
	(S)	(A)	(B)	(V)	T = A+B+V	(X = S - T)	(L)	(X/L)
Debbie	$18.00	$4.90	$4.05	$2.25	$11.20	$6.80	0.45	$15.11
Trish	$6.50	$1.80	$1.89	$1.05	$4.74	$1.76	0.21	$8.38
Sarah	$30.00	$9.74	$6.75	$3.75	$20.24	$9.76	0.75	$13.01
Mike	$15.00	$4.20	$4.95	$2.75	$11.90	$3.10	0.55	$5.64
Sewing Kit	$10.20	$5.40	$1.44	$0.80	$7.64	$2.56	0.16	$16.00

Part 4 – Highest total contribution margin the company can earn to make optimal use of constrained resource

We need to first give ranking for the products based on the contribution margin per direct labor hour since labor hour is the constrained resource i.e. limiting factor. And then we will calculate the optimal units can be produced by using limiting factor and limiting sales demand.

Product	Contribution Margin per DLH (from part 4)	Ranking	Maximum Demand	DLH per unit	Total Hours Needed	maximum Hours available	DL Hours used in Otimal Production on the basis of ranking	Maximum Contribution Margin
	(A)			(D)	(I)		(P=D*I)	(A*P)
Debbie	$15.11	2	72000	0.45	32400		32400	$489,564
Trish	$8.38	4	64000	0.21	13440		13440	$112,627
Sarah	$13.01	3	57000	0.75	42750		42750	$556,178
Mike	$5.64	5	40000	0.55	22000		11000 (Balancing Figure)	$62,040
Sewing Kit	$16.00	1	347000	0.16	55520		55520	$888,320
					166110	155,110	155110	$2,108,729

The maximum contribution margin = $2,108,729

Note --- I have rounded off the contribution margin per direct labor hour to 2 decimal palces..in case difference in answer pls let me know so that I will provide you the complete answer without rounded off the decimal places

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