The Walton Toy Company manufactures a line of dolls and a doll dress sewing kit.

Question

The Walton Toy Company manufactures a line of dolls and a doll dress sewing kit. Demand for the dolls 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:

  

The following additional information is available:   

4. What is the highest total contribution margin that the company can earn if it makes optimal use of its constrained resource?

I have all of the other questions answered. I got $521,170, but it keeps saying it's wrong. Please show work, so I know what I was doing wrong.

Product Demand
Next year
(units) Selling
Price
per Unit Direct
Materials Direct
Labor Debbie 50,000 $13.50 $4.30 $3.20 Trish 42,000 $ 5.50 $1.10 $2.00 Sarah 35,000 $21.00 $6.44 $5.60 Mike 40,000 $10.00 $2.00 $4.00 Sewing kit 325,000 $ 8.00 $3.20 $1.60

Explanation / Answer

Walton Toy Company

Determination of contribution margin per unit and per direct labor hour for all the products:

Product

selling price per unit

Direct material cost per unit

Direct labor cost per unit

Variable overhead per unit

Total variable cost per unit

Contribution margin per unit

direct labor hours per unit

contribution per direct labor hour

Debbie

$13.50

$4.30

$3.20

$0.80

$8.30

$5.20

0.40 hours

$13.00

Trish

$5.50

$1.10

$2

$0.50

$3.60

$1.90

0.25 hours

$7.60

Sarah

$21

$6.44

$5.60

$1.40

$13.44

$7.56

0.70 hours

$10.80

Mike

$10

$2

$4

$1.00

$7.00

$3.00

0.50 hours

$6.00

Sewing Kit

$8

$3.20

$1.60

$0.40

$5.20

$2.80

0.20 hours

$14.00

Notes :

Total direct labor hour per unit/direct labor hour

Direct labor hour rate = $8 per hour

For instance, direct labor hour for the product Debbie = $3.20/$8 =0.4 hours

Contribution per direct labor hour = contribution per unit/direct labor hours per unit

For instance, contribution per direct labor hour for the product Sarah is arrived at as follows,

Contribution per unit = $7.56; direct labor hours per unit = 0.70 hours

Contribution per direct labor hour = $7.56/0.70 hours =$10.80

Accordingly, the contribution per direct labor hour for each product and respective ranking is as follows,

Product

Contribution per direct labor hour

Ranking

Debbie

$13.00

II

Trish

$7.60

IV

Sarah

$10.80

III

Mike

$6.00

V

Sewing Kit

$14.00

I

Since the product Sewing Kit earns highest contribution per direct labor hour, available direct labor hours are to allotted first for the production of the expected units of Sewing Kit.

Total available direct labor hours at the plant = 130,000 hours

Sewing Kit –

Demand in units for next year      325,000

Direct labor hour per unit            0.20 hours

Direct labor hours needed to produce 325,000 units = 325,000 x 0.2 hours = 65,000 hours

Remaining direct labor hours at plant = 130,000 – 65,000 = 65,000

The next product with highest ranking is Debbie.

Debbie –

Demand in units for next year      50,000

Direct labor hours per unit           0.40

Direct labor hours needed to produce 50,000 units = 50,000 x 0.40 = 20,000 hours

Remaining direct labor hours at plant = 65,000 – 20,000 = 45,000

The next product in terms of highest ranking is Sarah.

Sarah –

Demand in units for next year      35,000

Direct labor hours per unit           0.70 hours

Direct labor hours needed to produce 35,000 units = 35,000 x 0.70 = 24,500 hours

Remaining direct labor hours at plant = 45,000 – 24,500 = 20,500 hours

The next product in terms of highest ranking is Trish.

Trish –

Demand in units for next year      42,000

Direct labor hours per unit           0.25 hours

Direct labor hours needed to produce 42,000 units = 42,000 x 0.25 = 10,500 hours

Remaining direct labor hours at plant = 20,500 – 10,500 = 10,000 hours

The product with the least ranking is Mike.

Mike –

Demand in units for next year      40,000

Direct labor hours per unit           0.50

Direct labor hours needed to produce 40,000 units = 40,000 x 0.50 = 20,000 hours

However, the available direct labor hours are 10,000

Hence, the number of units of Mike that can be produced with the available direct labor hours = 10,000 hrs/0.50 hrs

= 20,000 units

Computation of the highest total contribution margin that the company can earn by making the optimal use of constrained resource:

Product

Units

Contribution margin per unit

Contribution margin

Debbie

50,000

$5.20

$260,000

Trish

42,000

$1.90

$79,800

Sarah

35,000

$7.56

$264,600

Mike

20,000

$3.00

$60,000

Sewing Kit

325,000

$2.80

$910,000

Total contribution            $1,574,400

Less: Fixed costs              $520,000

Net operating income       $1,054,400

Product

selling price per unit

Direct material cost per unit

Direct labor cost per unit

Variable overhead per unit

Total variable cost per unit

Contribution margin per unit

direct labor hours per unit

contribution per direct labor hour

Debbie

$13.50

$4.30

$3.20

$0.80

$8.30

$5.20

0.40 hours

$13.00

Trish

$5.50

$1.10

$2

$0.50

$3.60

$1.90

0.25 hours

$7.60

Sarah

$21

$6.44

$5.60

$1.40

$13.44

$7.56

0.70 hours

$10.80

Mike

$10

$2

$4

$1.00

$7.00

$3.00

0.50 hours

$6.00

Sewing Kit

$8

$3.20

$1.60

$0.40

$5.20

$2.80

0.20 hours

$14.00

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