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	55,000	$	27.00	$	4.80	$	5.00
Trish	47,000	$	6.00	$	1.60	$	1.50
Sarah	40,000	$	40.00	$	7.19	$	8.00
Mike	35,000	$	15.00	$	2.50	$	6.00
Sewing kit	330,000	$	8.50	$	3.70	$	1.00

The following additional information is available:  

1. The company’s plant has a capacity of 110,050 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 $10 per hour is expected to remain unchanged during the coming year.

3. Fixed manufacturing costs total $570,000 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.

Answer 1

The Company produces 5 Products. We have to determine the best Economical Sales & Production Mix for the coming year.

Let us first find out the most profitable product of the company. Contribution per Unit will be the best measure to find out the most profitable product in the given scenario.

Now,

Contribution per Unit = Sales Price Per Unit - Variable Cost Per Unit

Here, Variable Cost = Direct Material Cost + Direct Labour + Variable Overhead

Now, using the above formula, let us calculate Variable Cost per Unit of all the Products manufactured by the Company.

1. Debbie - Direct Material Cost - $ 4.8 / Unit

Direct Labour Cost - $ 5 / Unit

Variable Overhead - $ 2 / Unit (0.5 Hours / Unit * $ 4 per labour Hour)

Therefore, Total Variable Cost for manufacturing 1 Unit of Debbie = $ 4.8 + $ 5 +$ 2 = $ 11.8 / Doll

2. Trish -   Direct Material Cost - $ 1.6 / Unit

    Direct Labour Cost - $ 1.5 / Unit

Variable Overhead - $ 0.6 / Unit (0.15 Hours / Unit * $ 4 per labour Hour)

Therefore, Total Variable Cost for manufacturing 1 Unit of Trish = $ 1.6 + $ 1.5 +$ 0.6 = $ 3.7 / Doll

3. Sarah -   Direct Material Cost - $ 7.19 / Unit

Direct Labour Cost - $ 8 / Unit

Variable Overhead - $ 3.2 / Unit (0.80 Hours / Unit * $ 4 per labour Hour)

Therefore, Total Variable Cost for manufacturing 1 Unit of Sarah = $ 7.19 + $ 8 +$ 3.2 = $ 18.39 / Doll

4. Mike -   Direct Material Cost - $ 2.5 / Unit

Direct Labour Cost - $ 6 / Unit

Variable Overhead - $ 2.4 / Unit (0.60 Hours / Unit * $ 4 per labour Hour)

Therefore, Total Variable Cost for manufacturing 1 Unit of Mike = $ 2.5 + $ 6 +$ 2.4 = $ 10.90 / Doll

5. Sewing Kit - Direct Material Cost - $ 3.7 / Unit

Direct Labour Cost - $ 1 / Unit

Variable Overhead - $ 0.4 / Unit (0.10 Hours / Unit * $ 4 per labour Hour)

Therefore, Total Variable Cost for manufacturing 1 Unit Sewing Kit = $ 3.7 + $ 1 +$ 0.40 = $ 5.10 / Sewing Kit

Now, we have the Variable Costs of all the products.

Further, as discussed before, let us now calculate the Contribution per Unit to find out the most profitable product of the Company.

Contribution = Sales Price Per Unit - Variable Cost per Unit

Contribution of all the products is calculated as below :

1. Debbie = $ 27 - $ 11.8 = $ 15.20 / Doll (Rank II)

2. Trish = $ 6 - $ 3.7 = $ 2.30 / Doll (Rank V)

3. Sarah = $ 40 - $ 18.39 = $ 21.61 / Doll (Rank I)

4. Mike = $ 15 - $ 10.90 = $ 4.10 / Doll (Rank III)

5. Sewing Kit = $ 8.5 - $ 5.10 = $ 3.40 / Sewing Kit (Rank IV)

From the above calculation, it can be determined that the most profitable product is Sarah and the least profitable is Trish. Ranks is allotted based on the per unit contribution of the product. These Ranks will be used while determining the Economical & Production Mix for the Company.

Now, the company has total of 1,10,050 Direct Labour Hours per Year. Also, the demand of the products for the next year is available.

(It should be noted that the company should not produce more than the demand of the products (though more profitable),as it will result into piling of stock and opportunity loss of the demand of the other products.)

Let us now find out the Economical Sales & Production Mix for the Company.

'Sarah' should be produced first being the most profitable product.

Total Demand of Sarah in the coming Year is 40,000 Units.

Labour Hours Required to Produce 1 Unit = 0.80 Hours Per Unit ($8 per Unit / $10 per Hour)

Hence, total Hours required to satisfy the demand of 'Sarah' = 40,000 Units * 0.80 Hour per Unit = 32,000 Hours.

Now, total hours remaining after manufacturing 'Sarah' = 1,10,050 - 32,000 = 78,050 Hours

Now, further, the company should produce Debbie, being the second most profitable product.

Total Demand of Debbie in the coming Year is 55,000 Units.

Labour Hours Required to Produce 1 Unit = 0.50 Hours Per Unit ($5 per Unit / $10 per Hour)

Hence, total Hours required to satisfy the demand of 'Debbie' = 55,000 Units * 0.50 Hour per Unit = 27,500 Hours.

Now, total hours remaining after manufacturing 'Debbie & Sarah' = 78,050 - 27,500 = 50,550 Hours

Next, the company should produce 'Mike', based on ranking.

Total Demand of 'Mike' in the coming Year is 35,000 Units.

Labour Hours Required to Produce 1 Unit = 0.60 Hours Per Unit ($6 per Unit / $10 per Hour)

Hence, total Hours required to satisfy the demand of 'Mike' = 35,000 Units * 0.60 Hour per Unit = 21,000 Hours.

Now, total hours remaining after manufacturing 'Mike, Debbie & Sarah' = 50,550 - 21,000 = 29,550 Hours

Next, the company should produce Sewing Kit, based on ranking.

Total Demand of 'Sewing Kit' in the coming Year is 3,30,000 Units.

Labour Hours Required to Produce 1 Unit = 0.10 Hours Per Unit ($1 per Unit / $10 per Hour)

Hence, total Hours required to satisfy the demand of 'Sewing Kit' = 3,30,000 Units * 0.10 Hour per Unit = 33,000 Hours.

However, total hours remaining is 29,550. Hence, the company will not be able to satisfy full demand of Sewing Kit. The maximum Units of Sewing Kit the company will be able to manufacture is 29,500 Hours / 0.1 Hour per Unit = 2,95,000 Units.

Hence, below is the best Production Mix for the Company :

Sarah = 40,000 Units

Debbie = 55,000 Units

Mike = 35,000 Units

Sewing Kit = 2,95,000 Units

Trish = 0 Units (due to time constraint)

Below is the total profit that can be earned by the company in the coming year =

Total Contribution :

Sarah = 40,000 Units * 21.61 per Unit = $ 8,64,400

Debbie = 55,000 Units * 15.20 per Unit = $ 8,36,000

Mike = 35,000 Units * 4.1 per Unit = $ 1,43,500

Sewing Kit = 2,95,000 * 3.40 per Unit = $ 10,03,000

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Total Contribution = $ 28,46,900

Less: Fixed Cost = $ 5,70,000

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Total Profit of the Company = $ 22,76,900

It is hereby concluded that following is the Economical Sales & Production Mix of Walton Toy Company for the Coming Year :

Company should manufacture 40,000 Units of 'Sarah Dolls', 55,000 Units of 'Debbie Dolls', 35,000 Units of 'Mike Dolls' and 2,95,000 Units of Sewing Kits.