Question 1 (50 Marks) Sherpa Sensors Pty Ltd manufactures hightech temperature sensors for various medical purposes, such as MRI imaging equipment and ultrasound scanners, and electronic applications, such as electrical appliances. There are four distribution methods for the temperature sensors, as shown in Table 1. Because of differing distribution and promotional costs, the product's profitability will vary with the distribution method. In addition, the advertising cost and the personal sales effort required will vary with the distribution method. The following table summarises the sensors' contribution to profit, advertising cost, and personal sales effort. Personal 'Sales Effort Profit per Unit Advertlsmg Cost per per Unit Sold Sold ($) Unit Sold (55) (minutes) Medical distributors 900 50 Electrical distributors 850 8 23 National retail stores 700 9 25 820 15 1 Distribution Method Sherpa Sensors Pty Ltd has set the advertising budget at $65000, and a maximum of 3000 hours of salesforce time is available forthe sales effort at the cost of $45/hour. Management also decided to produce exactly 6000 sensors for the current production period. Finally, an ongoing contract with the national chain of retail stores requires that at least 1500 units be distributed through this distribution method. Sherpa Sensors Pty Ltd needs to establish a strategy that will provide for the distribution of the sensors to maximise the overall profitability of the sensor production. Decisions must be made about how many units should be allocated to each of the four distribution methods and how to allocate the advertising budget and salesforce effort to each ofthe four distribution methods. For the situation given above: a) Determine the decision variables and describe your reasoning. (5 marks) b) Formulate the situation into a Mathematical Programming problem. (5 marks) c) Explain what type of Mathematical Programming problem it is formulated as. (5 mark) d) Find the optimal solution using Microsoft Excel's Solver. Include the answer report in your file. (10 marks) {D V Are all the distribution methods used for the solution found in (d)? If not, should management consider removing one of the distribution methods? If yes, what can the management do to improve the profit further? (10 marks) -n U What would your recommendation be regarding the contractual commitment to the retail stores for the solution found in (d)? For example, could they be more profitable if they reduced or increased their level of commitment (i.e. the minimum number of units sold)? (10 marks) Listthe binding and non-binding constraints forthe optimal solution in (d). (5 marks) G2 V