- 10 Marks
Question
Unity Company Ltd is preparing for next season’s operations. The company has provided the following information relating to its three products:
| TO | GE | DA | |
|---|---|---|---|
| Selling Price | GH¢18.5 | GH¢16.2 | GH¢12.6 |
| Material Cost (@ GH¢1.75 per kg) | GH¢8.75 | GH¢10.5 | GH¢3.5 |
| Labour Cost (@ GH¢2.2 per labour hour) | GH¢7.7 | GH¢4.4 | GH¢7.7 |
| Annual Demand | 2,150 units | 3,235 units | 1,556 units |
The company can only make available a total of 18,560 hours in the short run.
Required:
i) Provide the optimal production plan for Unity Ltd for the ensuing period.
(5 marks)
ii) What is the total incremental benefit of producing DA instead of GE, assuming available resources can only meet the demand for DA?
(3 marks)
iii) Indicate the shadow price of the production plan and state the basic assumption under which this price will apply.
(2 marks)
Answer
i) Optimal Production Plan:
- Labour hours required to meet demand:
- TO: 2,150 units×3.5 hours/unit=7,525 hours2,150 \text{ units} \times 3.5 \text{ hours/unit} = 7,525 \text{ hours}
- GE: 3,235 units×2.0 hours/unit=6,470 hours3,235 \text{ units} \times 2.0 \text{ hours/unit} = 6,470 \text{ hours}
- DA: 1,556 units×3.5 hours/unit=5,446 hours1,556 \text{ units} \times 3.5 \text{ hours/unit} = 5,446 \text{ hours}
Total required hours: 19,441 hours (exceeds available hours).
- Contribution per labour hour:
- TO: Contribution per unit = GH¢2.05, Contribution per labour hour = 2.053.5=0.59\frac{2.05}{3.5} = 0.59
- GE: Contribution per unit = GH¢1.30, Contribution per labour hour = 1.302=0.65\frac{1.30}{2} = 0.65
- DA: Contribution per unit = GH¢1.40, Contribution per labour hour = 1.403.5=0.40\frac{1.40}{3.5} = 0.40
Ranking: GE (1st), TO (2nd), DA (3rd).
- Resource Allocation (18,560 hours):
- GE: 3,235 units×2.0 hours/unit=6,470 hours3,235 \text{ units} \times 2.0 \text{ hours/unit} = 6,470 \text{ hours}
- TO: 2,150 units×3.5 hours/unit=7,525 hours2,150 \text{ units} \times 3.5 \text{ hours/unit} = 7,525 \text{ hours}
- DA: 1,304.29 units×3.5 hours/unit=4,565 hours1,304.29 \text{ units} \times 3.5 \text{ hours/unit} = 4,565 \text{ hours}
Total allocated hours: 18,560 hours.
ii) Total Incremental Benefit of Producing DA Instead of GE:
- Contribution per unit for DA = GH¢1.40
- Contribution per unit for GE = GH¢1.30
- Incremental Benefit per unit = GH¢0.10Total Incremental Benefit: 0.10×1,556 units=GH¢155.600.10 \times 1,556 \text{ units} = GH¢155.60
iii) Shadow Price and Assumptions:
- Shadow Price: GH¢0.40 (the contribution per limiting factor).
- Basic Assumption: This shadow price applies under the assumption that the additional resource can be obtained at the normal variable cost and that there are no changes in the product mix or external conditions.
- Uploader: Dotse