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Ace Electronics can produce four potential products: MP3 Players, CD
Players, Digital Radios and DVD players. There are three major inputs
for all products: electronic components, other components and assembly
time.
Electronic components cost $14 each, other components $10 each and
assembly time $20 per hour. Consumption of theses inputs per unit of
product together with total available monthly supply of components are
shown below:
|
MP3 Player |
CD Player |
Digital Radio |
DVD Player |
Available |
| Electronic components |
3 |
4 |
4 |
3 |
4,700 |
| Other components |
2 |
2 |
4 |
3 |
4,500 |
| Assembly hours |
1 |
1 |
3 |
2 |
2,500 |
Selling prices of the products are:
| Product |
Selling Price |
| MP3 Players |
$140 |
| CD Players |
$160 |
| Digital Radios |
$300 |
| DVD Players |
$220 |
Fixed costs per month amount to $12,000.
(a) Calculate the contribution margin for each product. (2 marks)
(b) If management wishes to produce and sell Mp3s, Cds, Digital
Radios and DVDs in the ratio 4:3:2:1, how many units of each should
management plan to produce and sell in a month to earn a profit before
tax of $70,000? (3 marks)
(c) Instead of producing the product mix in part (b), management
wishes to use linear programming to find the profit-maximising mix.
Write an LP model, and then use Excel’s Solver to determine the optimum
weekly mix and the resulting weekly profit before tax. (5 marks)
(d) Competitive pressures will probably force management to reduce
the price for DVD players. What is the maximum price reduction that can
be sustained such that the optimum mix calculated in part (c) remains
optimum? (2 marks)
(e) What is the shadow price for Electronic Components? Explain to
management how they might use this to increase profits? Calculate the
upper limit for which this shadow price is valid. What happens when the
upper limit is breached? (3 marks)
(f) Explain why linear programming is referred to as a resource
allocation technique? Give examples of three different types of problems
that can be solved via linear programming. (5 marks)
