Question

A company is able to produce four products and is planning its production mix for the next period.

Estimated cost, sales, and production data follow:

Product                                                       W                   X                    Y              Z

                                                                    ₤                    ₤                    ₤                 ₤

Selling Price/unit                                       29                  36                  61               51

Labour (@ ₤ 5/hr)                                    15                 10                  35                25

Material (@ ₤ 1/kg)                                   6                  18                  10               12    

Contribution                                              ₤8                 ₤8                 ₤16            ₤14

Resources/Unit                                            ₤                   ₤                   ₤                  ₤

Labour (hours)                                           3                    2                 7                  5

Materials (Kgs.)                                          6                    18                10               12

Maximum Demand (Units)                    5000                5000                5000          5000

Based on the above data, which is the most appropriate mix under the two following assumptions?

If labour hours are limited to 50,000 in a period or

If material is limited to 110,000 kgs in a period

Answer 1

Solution

Determination of the most appropriate product mix under the assumption of labor hours limited to 50,000 in a period:

Step1 – determine the contribution margin per labor hour for each product

Step 2 – rank the product in order of highest contribution margin per labor hour

Step 3 – assign labor hours based on the ranking above

Step 4 – determine the product mix and the profitability.

	W	X	Y	Z
labor hours needed per unit	3	2	7	5
contribution margin per unit	£8	£8	£16	£14
Contribution margin per labor hour	£2.67	£4	£2.29	£2.8
Ranking	III	I	IV	II
Maximum demand	5,000	5,000	5,000	5,000
maximum hours needed	15,000	10,000	35,000	25,000
Assigned labor hours	15,000	10,000	0	25,000
Product Mix	5,000	5,000	0	5,000

	Labor hours limited
	W	X	Y	Z
Production mix (units)	5,000	5,000	0	5,000
Contribution margin per unit	£8	£8	£16	£14
Total contribution margin	£40,000	£40,000	0	£70,000
Total optimal contribution margin = 40,000 + 40,000 + 70,000 = £150,000

Computations & notes:

Step 1 –

Determination of contribution margin per labor hour for each product:

Contribution margin per labor hour = contribution margin per unit/hours needed per unit

	W	X	Y	Z
labor hours needed per unit	3	2	7	5
contribution margin per unit	£8	£8	£16	£14
Contribution margin per labor hour	8/3 =£2.67	8/2 =£4	16/7 = £2.29	14/5 = £2.8

Step 2 –

Based on the above contribution margin per labor hour, product X earns highest contribution margin per labor hour followed by Product Z, Product W and Product Y.

Step 3:

Based on the ranking above, the limited labor hours are first allocated to Product X (5,000 x 2 = 10,000 hours);

Product Z (5,000 x 5 = 25,000 hours) and the remaining 15,000 hours are entirely allocated for the production of Product W (5,000 x 3 = 15,000 hours).

No more labor hours are available for the production of Product Y.

Since, there is no mention of a requirement to produce certain minimum units of each product, Product Y is not produced.

Material is limited –

Determination of the most appropriate product mix under the assumption of material is limited to 110,000 Kgs in a period:

Step1 – determine the contribution margin per Kg of material for each product

Step 2 – rank the product in order of highest contribution margin per Kg of material

Step 3 – assign material based on the ranking above

Step 4 – determine the product mix and the profitability.

	W	X	Y	Z
Material (Kg) needed per unit	6	18	10	12
contribution margin per unit	£8	£8	£16	£14
Contribution margin per Kg of material	£1.33	£0.44	£1.60	£1.17
Ranking	II	IV	I	III
Maximum demand	5,000	5,000	5,000	5,000
maximum material (Kg) needed	30,000	90,000	50,000	60,000
Assigned material (Kg)	30,000	0	50,000	30,000
Product Mix	5,000	0	5,000	2,500

Computations & notes:

Step 1 –

Determination of contribution margin per Kg of material for each product:

Contribution margin per Kg of material = contribution margin per unit/material needed per unit

	W	X	Y	Z
material needed per unit	6	18	10	12
contribution margin per unit	£8	£8	£16	£14
Contribution margin per labor hour	8/6 =£1.33	8/18 =£0.44	16/10 = £1.60	14/12 = £1.17

Step 2 –

Based on the above contribution margin per Kg of material, product Y earns highest contribution margin per material Kg followed by Product W, Product Z and Product X.

Step 3:

Based on the ranking above, the limited material (Kg) is first allocated to Product Y (5,000 x 10 = 50,000 Kg);

Product W (5,000 x 6 = 30,000 Kg) and the remaining 30,000 hours are entirely allocated for the production of Product Z (30,000 Kg/12 = 2,500 units).

No more material is available for the production of Product X.

Since, there is no mention of a requirement to produce certain minimum units of each product, Product X is not produced.

Hence, the optimal product mix and profitability is as follows,

	Material (Kg) limited
	W	X	Y	Z
Production (units)	5,000	0	5,000	2,500
Contribution margin per unit	£8	£8	£16	£14
Total contribution margin	£40,000	0	£80,000	£35,000
Total contribution margin = £40,000 + 0 + £80,000 +£35,000 = £155,000