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	65,000	$	28.00	$	4.20	$	4.05
Trish	57,000	$	6.00	$	1.10	$	1.26
Sarah	50,000	$	35.00	$	8.69	$	6.75
Mike	40,000	$	14.00	$	3.50	$	4.95
Sewing kit	340,000	$	9.50	$	4.70	$	0.81

The following additional information is available:  

The company’s plant has a capacity of 116,330 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 $535,000 per year. Variable overhead costs are $2 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 116,330 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

First four questions have been answered:

Part 1
Since direct labour rate is $9 per hour hence, direct labour hours required to produce each unit of five are calculate below:
Product	Direct labour ($)	Direct labour hour	Direct labour hour (Hour)
Debbie	4.05	(1 x 4.05/9)	0.45
Trish	1.26	(1 x 1.26/9)	0.14
Sarah	6.75	(1 x 6.75/9)	0.75
Mike	4.95	(1 x 4.95/9)	0.55
Sewing kit	0.81	(1 x 0.81/9)	0.09
Part 2:
Product	Direct labour hour (Hour)	Variable overhead cost @2 per hour ( 2 x direct labour hour)
Debbie	0.45	0.9
Trish	0.14	0.28
Sarah	0.75	1.5
Mike	0.55	1.1
Sewing kit	0.09	0.18

Part 3:
Product	(A): Selling price per unit	(B): direct materials	(C)Direct labour	(D): Contribution {A - (B + C)}	(E)Direct labour hour (Hour)	(F): Contribution margin per direct labour hour (D / E)
Debbie	28	4.2	4.05	19.75	0.45	43.88889
Trish	6	1.1	1.26	3.64	0.14	26
Sarah	35	8.69	6.75	19.56	0.75	26.08
Mike	14	3.5	4.95	5.55	0.55	10.09091
Sewing kit	9.5	4.7	0.81	3.99	0.09	44.33333

Part 4:
Ranking on the basis of contribution per direct labour hour
Product	(F): Contribution margin per direct labour hour (D / E)	Ranking	Number of units to be produced	(E)Direct labour hour (Hour)	Direct labours used
Debbie	43.88889	2	65000	0.45	29250
Trish	26	4	57000	0.14	7980
Sarah	26.08	3	50000	0.75	37500
Mike	10.09091	5		0.55
Sewing kit	44.33333	1	340000	0.09	30600
					105330

Total available direct labour hours	116330
Less; Used in 4 products	105330
Direct labour hours available for Mike	11000
Labour hour each unit of Mike	0.55
Number of units to be produced (11000 / 0.55)	20000

Thus, number of units of different products to be produced to earn highest contribution considering the constraining factor of availability of direct labour hours are as following:   

Ranking on the basis of contribution per direct labour hour
Product	(F): Contribution margin per direct labour hour (D / E)	Ranking	Number of units to be produced	(E)Direct labour hour (Hour)	Direct labours used
Debbie	43.88889	2	65000	0.45	29250
Trish	26	4	57000	0.14	7980
Sarah	26.08	3	50000	0.75	37500
Mike	10.09091	5	20000	0.55	11000
Sewing kit	44.33333	1	340000	0.09	30600
					116330