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	50,000	$	16.70	$	4.30	$	6.40
Trish	42,000	$	7.50	$	1.10	$	4.00
Sarah	35,000	$	26.60	$	6.44	$	11.20
Mike	40,000	$	14.00	$	2.00	$	8.00
Sewing kit	325,000	$	9.60	$	3.20	$	3.20

The following additional information is available:  

The company’s plant has a capacity of 130,000 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 $16 per hour is expected to remain unchanged during the coming year.

Fixed manufacturing costs total $520,000 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 130,000 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

1.

Direct labor hours = direct labor cost / direct labor rate per hour
	Direct labor cost per unit(A)	Direct labor hour rate(B)	Direct labor hours required per unit (A/B)
debbie	6.4	16	0.4
trish	4	16	0.25
sarah	11.2	16	0.7
Mike	8	16	0.5
Sewing kit	3.2	16	0.2

2.

Calculation of variable overhead cost
Particulars	debbie	trish	sarah	Mike	Sewing kit
Variable ovehead cost ( $ 2 X direct labor hr per unit )	0.8	0.5	1.4	1	0.4
	2X.4	2X.25	2X.7	2X.5	2X.2

3.

Particulars	debbie	trish	sarah	Mike	Sewing kit
Selling price (a)	16.7	7.5	26.6	14	9.6
Variable cost:
Direct material	4.3	1.1	6.44	2	3.2
Direct labor	6.4	4	11.2	8	3.2
Variable overhead	0.8	0.5	1.4	1	0.4
Total variable cost(b)	11.5	5.6	19.04	11	6.8
Contribution (a-b)	5.2	1.9	7.56	3	2.8

4.

Contribution statement

Particulars	debbie	trish	sarah	Mike	Sewing kit
Selling price (a)	16.7	7.5	26.6	14	9.6
Variable cost:
Direct material	4.3	1.1	6.44	2	3.2
Direct labor	6.4	4	11.2	8	3.2
Variable overhead	0.8	0.5	1.4	1	0.4
Total variable cost(b)	11.5	5.6	19.04	11	6.8
(C)Contribution (a-b)	5.2	1.9	7.56	3	2.8
(d)direct labor hr	0.4	0.25	0.7	0.5	0.2
Contributionn per labor hr(c/d)	13	7.6	10.8	6	14
Ranking	2	4	3	5	1

Calculation of direct labor hours reuired to meet the demand

Product	Direct labor hours required per unit (A)	Maximum demand(B)	Total hours required(A*B)
debbie	0.4	50000	20000
trish	0.25	42000	10500
sarah	0.7	35000	24500
Mike	0.5	40000	20000
Sewing kit	0.2	325000	65000
Total hours required			140000

Direct labor hour required to meet the next year demand is 140000 labor hr but capacity of plant is 130000 labor hr . shortage of 10000 labor hour should be reduced by avoiding product havinf low contributio margin per direct labor hr. Mike's contrinbution margin is low and reduces this product production to 20000 units ( 10000 shortage hours divided by .0 hr per unut = 20000 units )

calculation of highest contribution margin if company makes optimal use of constrained resource.

Product	Unit contribution margin	Production plan	Total contribution margin
debbie	5.2	50000	260,000
trish	1.9	42000	79,800
sarah	7.56	35000	264,600
Mike	3	20000	60,000
Sewing kit	2.8	325000	910,000
Total			1,574,400

5.

To produce additional units of mike, the company will be willing to pay upto $ 14 per hour

$14 = $ 8(usual rate ) + $ 6 ( contribution margin per hr of mike)