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)