- 15 Marks
MA – L2 – Q47 – Decision Making Techniques
Question
An engineering company has been experiencing problems with restricted availability of resources. The company manufactures a variety of casings. It makes four types of casing. Each casing requires the same bought-in component and some high-grade steel. The standard costs for the four types of casing are as follows:
| Casing | A | B | C | D |
|---|---|---|---|---|
| GH₵ | GH₵ | GH₵ | GH₵ | |
| Steel | 250 | 500 | 190 | 390 |
| Bought-in component | 50 | 50 | 50 | 50 |
| Direct labour | 60 | 60 | 50 | 100 |
| Variable production costs | 40 | 50 | 40 | 50 |
| Fixed production costs | 180 | 240 | 150 | 270 |
| Selling and administration costs | 145 | 225 | 120 | 215 |
| Profit | 35 | 55 | 30 | 55 |
| Selling price | 760 | 1,180 | 630 | 1,130 |
All the selling and administration costs are fixed and the same single component is used for each of the four products. Direct labour is paid GH₵8 per standard hour and each member of the workforce is capable of producing any of the casings.
The company’s main customer has ordered 30 units of Casing A, 20 units of B, 30 units of C, and 20 units of D for production and delivery in the next month. Senior management have agreed that this order should be treated as a priority order and that these casings must be manufactured and delivered to the customer next month. This is necessary to maintain the goodwill of the customer. It is estimated that this order represents 10% of the total demand next month for each type of casing.
The company operates a just-in-time system, and has no inventories of steel, components, or finished goods.
Required:
If the aim is to maximise profit for the month, establish the production and selling plan for the company next month in the following situation:
(a) Situation 1. Supplies of steel are limited to GH₵250,000.
(b) Situation 2. Only 400 bought-in components are available from suppliers.
(c) Situation 3. A labour dispute restricts available productive labour hours in the month to 2,125.
(d) Situation 4. A labour dispute restricts available productive labour hours in the month to 2,125; but the manufacture of any quantities of the four casings could be sub-contracted to an outside supplier. The cost of buying the casings externally would be GH₵475, GH₵705, GH₵380, and GH₵640 for Casing A, Casing B, Casing C, and Casing D respectively. In addition, it should be assumed that the major customer insists that its order is completed by the company itself and the manufacture should not be subcontracted.
Answer
(A)
Working: Contribution per unit
| Casing | Selling price | Variable costs | Contribution per unit |
|---|---|---|---|
| A | 760 | 400 (250+50+60+40) | 360 |
| B | 1,180 | 660 (500+50+60+50) | 520 |
| C | 630 | 330 (190+50+50+40) | 300 |
| D | 1,130 | 590 (390+50+100+50) | 540 |
Resources required for the priority order for the major customer
| Casing | Units | Steel GH₵ | Components | Labour hours |
|---|---|---|---|---|
| A | 30 | 7,500 | 30 | 225 (30 × 7.5) |
| B | 20 | 10,000 | 20 | 150 (20 × 7.5) |
| C | 30 | 5,700 | 30 | 187.5 (30 × 6.25) |
| D | 20 | 7,800 | 20 | 250 (20 × 12.5) |
| Total | 31,000 | 100 | 812.5 |
(a) Steel in short supply and restricted to GH₵250,000
| Casing | Contribution/unit | Steel/unit | Contribution/steel | Ranking for manufacture |
|---|---|---|---|---|
| A | GH₵360 | GH₵250 | GH₵1.44 | 2nd |
| B | GH₵520 | GH₵500 | GH₵1.04 | 4th |
| C | GH₵300 | GH₵190 | GH₵1.58 | 1st |
| D | GH₵540 | GH₵390 | GH₵1.38 | 3rd |
Profit-maximising production schedule
| Steel used | A | B | C | D |
|---|---|---|---|---|
| units | units | units | units | |
| Priority order | 30 | 20 | 30 | 20 |
| Sales of C (balance) | 270 | |||
| Total production/sales | 30 | 20 | 300 | 20 |
Explanation:
- Total steel available: GH₵250,000.
- Steel required for priority order: GH₵31,000.
- Steel remaining: GH₵250,000 – GH₵31,000 = GH₵219,000.
- Total demand (priority order is 10% of demand): A: 300 units, B: 200 units, C: 300 units, D: 200 units.
- Ranking based on contribution per GH₵ of steel: C (1.58), A (1.44), D (1.38), B (1.04).
- After priority order, produce C (highest contribution per steel): 270 units × GH₵190 = GH₵51,300 steel.
- Total steel used: GH₵31,000 + GH₵51,300 = GH₵82,300 (within limit).
- No further steel available for A, D, or B.
(b) Components are in short supply and restricted to 400 units
Casing Contribution/unit Components/unit Contribution/component Ranking for manufacture A GH₵360 1 GH₵360 3rd B GH₵520 1 GH₵520 2nd C GH₵300 1 GH₵300 4th D GH₵540 1 GH₵540 1st Profit-maximising production schedule
Components used A B C D units units units units Priority order 30 20 30 20 Sales of D 180 280 Balance: Sales of B 120 Total available 400 Total production/sales 30 140 30 200 Explanation:
- Total components available: 400.
- Components required for priority order: 30 (A) + 20 (B) + 30 (C) + 20 (D) = 100.
- Components remaining: 400 – 100 = 300.
- Total demand: A: 300 units, B: 200 units, C: 300 units, D: 200 units.
- Ranking based on contribution per component: D (GH₵540), B (GH₵520), A (GH₵360), C (GH₵300).
- After priority order, produce D: 180 units (200 – 20) = 180 components.
- Remaining components: 300 – 180 = 120.
- Produce B: 120 units.
- Total production: A: 30, B: 140 (20 + 120), C: 30, D: 200 (20 + 180).
(c) Labour is in short supply and restricted to 2,125 hours
Casing Contribution/unit Labour hours/unit Contribution per hour Ranking for manufacture A GH₵360 7.5 GH₵48.00 2nd B GH₵520 7.5 GH₵69.33 1st C GH₵300 6.25 GH₵48.00 2nd D GH₵540 12.5 GH₵43.20 4th Profit-maximising production schedule
Labour hours A B C D units units units units Priority order 30 20 30 20 Sales of B 180 Sales of A or C 29 Total production/sales 59 200 30 20 Explanation:
- Total labour hours available: 2,125.
- Labour hours for priority order: 225 (A) + 150 (B) + 187.5 (C) + 250 (D) = 812.5 hours.
- Hours remaining: 2,125 – 812.5 = 1,312.5.
- Total demand: A: 300 units, B: 200 units, C: 300 units, D: 200 units.
- Ranking based on contribution per labour hour: B (GH₵69.33), A/C (GH₵48.00), D (GH₵43.20).
- After priority order, produce B: 180 units (200 – 20) × 7.5 = 1,350 hours (exceeds 1,312.5, adjust below).
- Correct allocation: Produce B: 174 units × 7.5 = 1,305 hours.
- Remaining hours: 1,312.5 – 1,305 = 7.5 (enough for 1 unit of A or C, but demand limits apply).
- Choose A (29 units remaining after priority) for simplicity.
- Total production: A: 59 (30 + 29), B: 200 (20 + 180), C: 30, D: 20.
(d) Make or buy decision
Casing Contribution/unit Labour hours/unit Contribution per hour Ranking for manufacture A GH₵360 7.5 GH₵48.00 2nd B GH₵520 7.5 GH₵69.33 1st C GH₵300 6.25 GH₵48.00 2nd D GH₵540 12.5 GH₵43.20 4th Casing Selling price Subcontract cost Contribution if subcontracted A 760 475 285 B 1,180 705 475 C 630 380 250 D 1,130 640 490 Profit-maximising production schedule
Labour hours A B C D units units units units Priority order (must make) 30 20 30 20 Sales of B (make) 180 Sales of A (buy) 270 Sales of C (buy) 270 Sales of D (buy) 180 Total production/sales 300 200 300 200 Explanation:
- Total labour hours available: 2,125.
- Labour hours for priority order: 812.5 hours (as calculated in Q47c).
- Hours remaining: 2,125 – 812.5 = 1,312.5.
- Total demand: A: 300 units, B: 200 units, C: 300 units, D: 200 units.
- Priority order cannot be subcontracted, so must be made in-house.
- Ranking for in-house production: B (GH₵69.33), A/C (GH₵48.00), D (GH₵43.20).
- After priority order, produce B: 180 units × 7.5 = 1,350 hours (exceeds 1,312.5).
- Adjust: Produce B: 174 units × 7.5 = 1,305 hours.
- Remaining hours: 7.5 (insufficient for significant production).
- Subcontract remaining demand: A (270 units), C (270 units), D (180 units).
- Contribution from subcontracting is positive for all, so subcontract to meet full demand.
- Total production: A: 300 (30 make, 270 buy), B: 200 (all make), C: 300 (30 make, 270 buy), D: 200 (20 make, 180 buy).
- Topic: Decision making techniques
- Uploader: Salamat Hamid