Question 7

A year or so ago Tom Tolkien invested in Drive Equip Plc, a new electric vehicle equipment company, which at the time had just been listed on the UKs Alternative Investment Market (AIM). After extensive research and development Drive Equip has just introduced an innovative navigation system which identifies the availability of electric vehicle charging points. The main distribution channel for the new product will be sales through specialist vehicle equipment distributors. However, the firm is also considering distributing the system using direct marketing.

The distribution and promotional costs differ, so the profitability of the product varies with the method selected. Using specialist vehicle distributors, the profit contribution per unit amounts to 120; if the company uses direct marketing the profit contribution rises to 160 per unit. In addition, the companys estimate of the advertising costs and sales time per unit sold will also vary with different distribution channels. The relevant information is summarised in the table, below.

	Specialist Distributor	Direct Marketing
Advertising cost per unit	24	36
Sales time per unit sold	5 hours	6 hours

Drive Equip management has specified that at least 1100 units must be distributed through direct marketing during the first three months. The company has set its advertising budget at 96,000 and has stated that a maximum of 24,000 hours of sales time will be available for the three-month planning period. In addition, production capacity for this period is 3000 units.

1. Formulate as a linear programming problem, where the aim is to determine the most profitable distribution strategy. (7 marks)

2. Solve the problem graphically and confirm algebraically, indicating the number of units that should be sold through each distribution channel (specialist distributors and direct marketing), and the maximum achievable profit contribution. (16 marks)

3. Explain precisely what is meant by the shadow price or dual value of a constraint, illustrating your answer with data from the Excel Sensitivity Report for the problem, which is provided below. (7 marks)

4. Using the Excel Sensitivity Report, identify the range of values for the profit contribution of the two distribution channels for which the optimal solution identified in (b) remains valid. (4 marks)

(Total: 35 marks)