MA – L2 – Q42 – Decision Making Techniques

Determine optimal production mix for four liquids with a contract obligation, maximizing profit within labour hour constraints.

Question

NexGen Ltd. manufactures four liquids: A, B, C, and D. The selling price and unit cost details for these products are as follows:

	Liquid A	Liquid B	Liquid C	Liquid D
	GH¢ per litre	GH¢ per litre	GH¢ per litre	GH¢ per litre
Selling price	100	120	120	110
Costs:
Direct materials	24	30	21	18
Direct labour (GH¢6/hour)	18	15	24	12
Direct expenses	0	0	0	0
Variable overhead	12	10	18	12
Fixed overhead (note 1)	24	20	36	24
Total cost per litre	78	75	102	66
Profit per litre	22	35	18	44

Note 1: Fixed overhead is absorbed on the basis of labour hours, based on a budget of 1,600 hours per quarter (three months).
During the next three months, the number of direct labour hours is expected to be limited to 1,345 hours. The same labour is used for all products.
The marketing director has identified the maximum demand for each of the four products during the next three months as follows:

Liquid A: 200 litres
Liquid B: 150 litres
Liquid C: 100 litres
Liquid D: 120 litres
No inventories are held at the beginning of the period that could be used to satisfy demand in the period.

Required:
(i) Determine the number of litres of liquids A, B, C, and D to be produced and sold in the next three months in order to maximise profits.
(ii) Calculate the profit that this would yield.

(B) Suppose that a contract has been made before the beginning of the period by NexGen Ltd. and one of its customers, PrimeCorp. NexGen Ltd. has agreed to supply PrimeCorp with 20 litres of each A, B, C, and D during the three-month period.
This sales demand from PrimeCorp is included in the demand levels shown above in part (a) of the question.

Required:
(i) Given the contract with PrimeCorp, determine the number of litres of liquids A, B, C, and D to be produced and sold in the next three months in order to maximise profits, if the maximum number of labour hours remain 1,345 hours for the period.
(ii) Calculate the profit that this would yield.

Answer

To maximize profits, we need to prioritize production based on the contribution per limiting factor (labour hours).

Step 1: Calculate labour hours per litre and contribution per litre

Labour cost per litre ÷ GH¢6/hour = hours per litre
Contribution = Selling price − Variable costs (Direct materials + Direct labour + Variable overhead)

	Liquid A	Liquid B	Liquid C	Liquid D
Selling price (GH¢)	100	120	120	110
Direct materials	24	30	21	18
Direct labour	18	15	24	12
Variable overhead	12	10	18	12
Total variable cost	54	55	63	42
Contribution/litre	46	65	57	68
Labour hours/litre (Labour cost ÷ GH¢6)	3	2.5	4	2
Contribution/hour (Contribution ÷ Hours)	15.33	26	14.25	34

Step 2: Rank products by contribution per labour hour

Liquid D: GH¢34/hour
Liquid B: GH¢26/hour
Liquid A: GH¢15.33/hour
Liquid C: GH¢14.25/hour

Step 3: Allocate labour hours to maximize contribution
Total labour hours available = 1,345 hours

Liquid D: Max demand 120 litres × 2 hours = 240 hours
Liquid B: Max demand 150 litres × 2.5 hours = 375 hours
Liquid A: Max demand 200 litres × 3 hours = 600 hours
Liquid C: Max demand 100 litres × 4 hours = 400 hours

Allocate hours in order of ranking:

Liquid D: 120 litres × 2 hours = 240 hours (Contribution: 120 × GH¢68 = GH¢8,160)
Liquid B: 150 litres × 2.5 hours = 375 hours (Contribution: 150 × GH¢65 = GH¢9,750)
Total hours used = 240 + 375 = 615 hours
Hours remaining = 1,345 − 615 = 730 hours

Allocate remaining hours to Liquid A (next highest contribution/hour):

Liquid A: 200 litres × 3 hours = 600 hours (uses 600 of 730 hours)
Contribution: 200 × GH¢46 = GH¢9,200
Hours remaining = 730 − 600 = 130 hours

Allocate remaining hours to Liquid C:

Liquid C: 130 hours ÷ 4 hours/litre = 32.5 litres (round to 32 litres for simplicity)
Contribution: 32 × GH¢57 = GH¢1,824

Step 4: Summarize production and contribution

Product	Litres	Hours	Contribution/litre (GH¢)	Contribution (GH¢)
D	120	240	68	8,160
B	150	375	65	9,750
A	200	600	46	9,200
C	32	128	57	1,824
Total		1,343		28,934

Step 5: Calculate profit
Total contribution = GH¢28,934
Fixed costs (based on 1,600 hours × GH¢12/hour, derived from fixed overhead rates) = 1,600 × GH¢12 = GH¢19,200
Profit = GH¢28,934 − GH¢19,200 = GH¢9,734

Final Answer:
(i) Produce:

Liquid D: 120 litres
Liquid B: 150 litres
Liquid A: 200 litres

Liquid C: 32 litres
(ii) Profit = GH¢9,734

(b) Step 1: Allocate hours to meet PrimeCorp contract
Contract requires 20 litres of each liquid:

Liquid A: 20 litres × 3 hours = 60 hours
Liquid B: 20 litres × 2.5 hours = 50 hours
Liquid C: 20 litres × 4 hours = 80 hours
Liquid D: 20 litres × 2 hours = 40 hours
Total hours for contract = 60 + 50 + 80 + 40 = 230 hours

Contribution from contract sales:

Liquid A: 20 × GH¢46 = GH¢920
Liquid B: 20 × GH¢65 = GH¢1,300
Liquid C: 20 × GH¢57 = GH¢1,140
Liquid D: 20 × GH¢68 = GH¢1,360
Total contribution from PrimeCorp = GH¢920 + GH¢1,300 + GH¢1,140 + GH¢1,360 = GH¢4,720

Step 2: Allocate remaining hours
Total hours available = 1,345
Hours used for contract = 230
Hours remaining = 1,345 − 230 = 1,115

Remaining demand after contract:

Liquid A: 200 − 20 = 180 litres
Liquid B: 150 − 20 = 130 litres
Liquid C: 100 − 20 = 80 litres
Liquid D: 120 − 20 = 100 litres

Allocate hours based on contribution per hour (from Q42a):

Liquid D: GH¢34/hour
Liquid B: GH¢26/hour
Liquid A: GH¢15.33/hour
Liquid C: GH¢14.25/hour
Liquid D: 100 litres × 2 hours = 200 hours (Contribution: 100 × GH¢68 = GH¢6,800)
Liquid B: 130 litres × 2.5 hours = 325 hours (Contribution: 130 × GH¢65 = GH¢8,450)
Total hours used = 200 + 325 = 525 hours
Hours remaining = 1,115 − 525 = 590 hours
Liquid A: 180 litres × 3 hours = 540 hours (Contribution: 180 × GH¢46 = GH¢8,280)
Hours remaining = 590 − 540 = 50 hours
Liquid C: 50 hours ÷ 4 hours/litre = 12.5 litres (round to 12 litres)
Contribution: 12 × GH¢57 = GH¢684

Step 3: Summarize production and contribution

Product	Litres	Hours	Contribution/litre (GH¢)	Contribution/profit (GH¢)
B	130	325	65	8,450
A	180	540	46	8,280
C (balance)	12	48	57	684
D	100	200	68	6,800
Subtotal		1,113		24,214
Contribution from sales to PrimeCorp				4,720
Total contribution				28,934
Fixed costs				19,200
Profit				9,734

Final Answer:
(i) Produce:

Liquid B: 130 litres
Liquid A: 180 litres
Liquid C: 12 litres
Liquid D: 100 litres
Plus 20 litres each of A, B, C, and D for PrimeCorp
(ii) Profit = GH¢9,734

Tags: Contract Obligations, Contribution Analysis, Labour Hours, Limiting Factors, Production Planning, Profit Maximization
Level: Level 2

Topic: Decision making techniques

Uploader: Salamat Hamid