- 16 Marks
Question
Manche produces two products from different quantities of the same resources using a just-in-time (JIT) production system. The selling price and resource requirements of each of the products are shown below:
| Product | C | L |
|---|---|---|
| Unit Selling Price (GH¢) | 130 | 160 |
| Resources per Unit: | ||
| Direct Labour (GH¢8 per hour) | 3 hours | 5 hours |
| Material A (GH¢3 per kg) | 5 kg | 4 kg |
| Material B (GH¢7 per litre) | 2 litres | 1 litre |
| Machine Hours (GH¢10 per hour) | 3 hours | 4 hours |
| Fixed Overhead (GH¢8 per hour) | 1 hour | 1 hour |
Market research shows that the maximum demand for products C and L during August 2024 is 500 units and 800 units respectively. This does not include an order that Manche has agreed with a commercial customer for the supply of 250 units of C and 350 units of L at selling prices of GH¢100 and GH¢135 per unit, respectively. Failure by Manche to deliver the order in full by the end of August will cause Manche to incur a GH¢5,000 financial penalty.
At a recent meeting between the Purchasing Manager and Production Manager to discuss the production plans of C and L for August, the following resource restrictions for the year were identified:
- Direct Labour Hours: 90,000 hours
- Machine Hours: 90,000 hours
The resource restrictions were evenly distributed throughout the year.
Required:
i) Prepare the optimum production plan for August 2024 using relevant computations.
ii) Determine the contribution from adopting this plan.
iii) Using relevant computations, show whether Manche should complete the order from the commercial customer assuming any excess labour hours for not making the contract can be used to produce 300 units of product ‘F’ with a contribution of GH¢55 per unit.
Answer
i) Optimum Production Plan
Identifying the Limiting Factor
- Monthly available labour hours: 90,000 ÷ 12 = 7,500 hours
- Monthly available machine hours: 90,000 ÷ 12 = 7,500 hours
| Product | Labour Hours Required |
|---|---|
| C (750 × 3) | 2,250 |
| L (1,150 × 5) | 5,750 |
| Total Required | 8,000 |
| Available | 7,500 |
| Shortage | 500 |
Labour hours are the limiting factor.
| Product | Contribution (GH¢/unit) | Labour Constraint (Hours/unit) | Contribution per Labour Hour (GH¢/hour) | Ranking |
|---|---|---|---|---|
| C | 47 | 3 | 15.67 | 1st |
| L | 61 | 5 | 12.20 | 2nd |
Since C has the highest contribution per labour hour, it is given priority in production.
| Production Order | Quantity | Labour Hours Used |
|---|---|---|
| C (Contract Order) | 250 | 750 |
| L (Contract Order) | 350 | 1,750 |
| C (Remaining Demand) | 500 | 1,500 |
| L (Remaining Demand) | 700 | Remaining Labour Hours (3,500) |
Total Labour Hours Used: 7,500 hours
ii) Contribution from the Adopted Plan
| Product | Quantity Produced | Contribution per Unit (GH¢) | Total Contribution (GH¢) |
|---|---|---|---|
| C (500 units) | 500 | 47 | 23,500 |
| L (700 units) | 700 | 61 | 42,700 |
| Total Contribution | 66,200 |
iii) Should Manche Complete the Order?
| Labour Hours Available | 7,500 |
|---|---|
| Hours Used for C and L Production | 5,500 |
| Excess Labour Hours | 2,000 |
- Contribution from Commercial Order (C & L):
| Product | Quantity | Contribution per Unit (GH¢) | Total Contribution (GH¢) |
|---|---|---|---|
| C (500 units) | 500 | 47 | 23,500 |
| L (800 units) | 800 | 61 | 48,800 |
| Total Contribution from C & L | 72,300 |
- Alternative Use of Labour Hours (Product F):
| Product | Quantity Produced | Contribution per Unit (GH¢) | Total Contribution (GH¢) |
|---|---|---|---|
| F | 300 | 55 | 16,500 |
- Financial Impact of Not Completing the Order:
| Contribution from C & L | 72,300 |
|---|---|
| Minus Penalty for Order Default | (5,000) |
| Net Contribution if Order is Rejected | 67,300 |
- Topic: Decision making techniques
- Series: Nov 2024
- Uploader: Salamat Hamid