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	67,000	$	30.00	$	4.40	$	4.40
Trish	59,000	$	5.40	$	1.30	$	0.80
Sarah	52,000	$	44.00	$	8.99	$	6.80
Mike	36,000	$	16.00	$	3.70	$	5.20
Sewing kit	342,000	$	9.70	$	4.90	$	0.40

The following additional information is available:  

1. The company’s plant has a capacity of 115,750 direct labor-hours per year on a single-shift basis. The company’s present employees and equipment can produce all five products.

2. The direct labor rate of $8 per hour is expected to remain unchanged during the coming year.

3. Fixed manufacturing costs total $555,000 per year. Variable overhead costs are $4 per direct labor-hour.

4. All of the company’s nonmanufacturing costs are fixed.

5. 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 115,750 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)
	Debbie	Trish	Sarah	Mike	Sewing kit
Direct Labor cost per unit (A)	$                      4.40	$                0.80	$                         6.80	$                5.20	$                 0.40
Direct Labor cost per hour(B)	$                      8.00	$                8.00	$                         8.00	$                8.00	$                 8.00
Direct Labor hour per unit(A / B)	$                      0.55	$                0.10	$                         0.85	$                0.65	$                 0.05
2)
Variable overhead cost per unit	Debbie	Trish	Sarah	Mike	Sewing Kit
Direct Labor hour per unit (A)	$                      0.55	$                0.10	$                         0.85	$                0.65	$                 0.05
Variable overhead cost per Direct Labor hour (B)	$                      4.00	$                4.00	$                         4.00	$                4.00	$                 4.00
Variable overhead cost per unit ($) (A x B)	$                      2.20	$                0.40	$                         3.40	$                2.60	$                 0.20
3)
Contribution margin per direct labor hour	Debbie	Trish	Sarah	Mike	Sewing Kit
Selling price per unit	$                    30.00	$                5.40	$                       44.00	$              16.00	$                 9.70
Direct Material per unit	$                      4.40	$                1.30	$                         8.99	$                3.70	$                 4.90
Direct Labor cost per unit	$                      4.40	$                0.80	$                         6.80	$                5.20	$                 0.40
Variable overhead cost per unit	$                      2.20	$                0.40	$                         3.40	$                2.60	$                 0.20
Contribution per unit ($) (A)	$                    19.00	$                2.90	$                       24.81	$                4.50	$                 4.20
Direct Labor hour per unit (B)	$                      0.55	$                0.10	$                         0.85	$                0.65	$                 0.05
Contribution per direct labor hour ($)(A/B)	$                    34.55	$              29.00	$                       29.19	$                6.92	$               84.00
4)
	Debbie	Trish	Sarah	Mike	Sewing Kit	Total
Contribution per direct labor hour (A)	$                    34.55	$              29.00	$                       29.19	$                6.92	$               84.00
Rank	2	4	3	5	1
Demand (Units) (B)	67,000	59,000	52,000	36,000	342,000
Direct Labor hour per unit ( c)	0.55	0.10	0.85	0.65	0.05
Resources to be Allocated (labour hours)(B X C)	36,850.00	5,900.00	44,200.00	23,400.00	17,100.00	127,450.00
Production Plan  (D)	67,000.00	59,000.00	52,000.00	18,000.00	342,000.00
Contribution per direct labor hour ($)(A x D)	$        2,314,545.45	$  1,711,000.00	$           1,517,788.24	$     124,615.38	$ 28,728,000.00
Total Contribution Margin	$      34,395,949.07
Direct labor hour required to produce next year’s demand is 127,450 but capacity of the plant is 115,750 labor hours. Shortage of 11,700 labor hours should be reduced by avoiding low contribution margin product. Mike’s contribution margin is low and reduces this product production to 18,000 units (11,700 exceed hours divided by 0.65 hours per unit = 18,000 units)
5)
Highest Price = $8 (the usual rate) + $6.92 (contribution margin per hour of Mike)	$                    14.92