Northern Hi-Tec Electronics Limited manufactures six computer peripheral devices: internal modems, external modems, circuit boards, CD drives, hard disk drives, and memory boards. The assembly processes are dynamic and a small variation in the input can cause a large fluctuation in the output. As a result of this, Northern Hi-Tec E. Ltd. tests the computer peripheral devices. Each of these technical products requires time, in minutes, on four types of electronic testing equipment, as shown in the following table:

Table: The time required, in minutes, on the electronic testing equipment

The first test device is available for 150 hours per week, the second device for 130 hours per week, the third device for 110 hours per week and the fourth device requires more preventive maintenance and may be used only for 102 hours each week. Northern Hi-Tec E. Ltd. Believes that the market for all six computer components is vast, and it can sell as many units of each product as it can manufacture. The table that follows summarises the selling price and material costs for each product:

BA2014 Coursework_Autumn_2011EMW Page 2

Table: Selling Prices and Material Costs per unit of the peripheral devices

In addition, variable labour costs are £25 per hour for test device 1, £15 per hour for test device 2, £18 per hour for test device 3, and £12 per hour for test device 4. Northern Hi-Tec E. Ltd. Wants to maximise its profits.

a) Calculate the contribution per unit (profit margin) for each computer peripheral device. (Hint: calculate the variable labour cost per unit for each peripheral device then calculate total variable cost). Show your calculations clearly and explain your answer in the context of the problem.

b) Develop a linear programming model which allows Northern Hi-Tec E. Ltd. to determine how many computer peripheral devices should be produced to maximise profits assuming that all peripheral devices can be sold. The model formulation should include the following:

i. Definition of the decision variables,

ii. Identification and formulation of the objective function,

iii. Identification and formulation of the constraints.

c) Solve the model you developed in part (b) using Excel's Solver. Clearly state value of the objective function and the optimal solution in the context of the problem.

d) Identify which of the constraint(s) are binding and which are not-binding. How much slack (surplus) do the not-binding constraint(s) have? Be specific and give your answer in the context of the problem.

e) If a reduction of £10 was made to the profit margin of 'Internal Modem', how would the optimal solution and value of the objective function change? Be specific and give your answer in the context of the problem.

f) What is the value of an additional minute of time per week on test device 1? Test device 2?

Test device 3? and Test device 4? Should Northern Hi-Tec E. Ltd. add more test device time? If so, on which Test device?

g) Write a short business report (of 1000 words) to advice Northern Hi-Tec E. Ltd. for its management decision. You will discuss the decision variables, constraints, optimal solutions, value of the objective function, slack variables, evaluate impact of changes on variable labour costs (as in e) and the production level and combination of the peripheral devices that help Northern Hi-Tec E. Ltd. maximise its profits.