The purpose of this assessment is to formulate and solve an optimisation problem for a local ABC communication company. ABC needs your help to solve a product distribution problem. Refer to the attached use case study of ABC. ABC manufactures portable radio systems that can be used for communications. ABC has many dealers in the following UAE cities: Abu Dhabi, Dubai, Sharjah and Ajman. ABC new product is suitable for use in a variety of business and personal applications. ABC sells its products through different dealers. The dealers for the new radio are as follows: 1. Abu Dhabi dealers 2. Dubai dealers 3. Sharjah dealers 4. Ajman dealers The profitability of the product will vary with the dealer channel. Also, the advertising cost and the personal sales effort required will vary with the dealer channel. The following table provides the advertising cost, profit and personal sales effort data relating to the ABC company. Advertising Cost per Dealer Abu Dhabi dealers Dubai dealers Sharjah dealers Ajman dealers Profit per Unit Sold (AED) 90 84 70 60 Unit Sold (AED) 10 8 Personal Sales Effort per Unit Sold (hours) 2 3 3 None 9 15 ABC company set the advertising budget at 5000 AED, and a maximum of 1800 hours of sales force time is available for allocation to the sales effort. ABC also decided to produce exactly 600 units for the current production period. ABC has an ongoing contract with Sharjah dealers that require at least 150 units be distributed through this distribution channel. ABC seeks your help to maximize its profit with the new product. 1. Formulate the mathematical model and critically explain your model. (CLO1, 30 Marks) 2. Using a software package, determine the optimal solution and provide an interpretation of the solution. (CLO1, 20 Marks) 3. Distinguish on whether the model produced slack/surplus variables. Include your interpretation to support your decision. (CLO2, 10 Marks) 4. Increasing the advertising budget may increase the profit of ABC. Investigate to what extend the advertising budget can be increased so that it will be beneficial to ABC. Discuss the profit that ABC will gain in this case. (CLO2, 15 Marks) 5. If management decides to increase the total unit production to 603, argue by how much the profit get increased. (CLO2, 10 Marks) 6. Management decided to increase the profit gained from Abu Dhabi dealers by 10 AED, Dubai dealers by 5 AED and Sharjah dealers by 5 AED. Argue on whether the optimal solution remains the same and support your answer with clear justification. Based on your arguments, deduce the new profit of ABC in this case. (CLO2, 15 Marks) The purpose of this assessment is to formulate and solve an optimisation problem for a local ABC communication company. ABC needs your help to solve a product distribution problem. Refer to the attached use case study of ABC. ABC manufactures portable radio systems that can be used for communications. ABC has many dealers in the following UAE cities: Abu Dhabi, Dubai, Sharjah and Ajman. ABC new product is suitable for use in a variety of business and personal applications. ABC sells its products through different dealers. The dealers for the new radio are as follows: 1. Abu Dhabi dealers 2. Dubai dealers 3. Sharjah dealers 4. Ajman dealers The profitability of the product will vary with the dealer channel. Also, the advertising cost and the personal sales effort required will vary with the dealer channel. The following table provides the advertising cost, profit and personal sales effort data relating to the ABC company. Advertising Cost per Dealer Abu Dhabi dealers Dubai dealers Sharjah dealers Ajman dealers Profit per Unit Sold (AED) 90 84 70 60 Unit Sold (AED) 10 8 Personal Sales Effort per Unit Sold (hours) 2 3 3 None 9 15 ABC company set the advertising budget at 5000 AED, and a maximum of 1800 hours of sales force time is available for allocation to the sales effort. ABC also decided to produce exactly 600 units for the current production period. ABC has an ongoing contract with Sharjah dealers that require at least 150 units be distributed through this distribution channel. ABC seeks your help to maximize its profit with the new product. 1. Formulate the mathematical model and critically explain your model. (CLO1, 30 Marks) 2. Using a software package, determine the optimal solution and provide an interpretation of the solution. (CLO1, 20 Marks) 3. Distinguish on whether the model produced slack/surplus variables. Include your interpretation to support your decision. (CLO2, 10 Marks) 4. Increasing the advertising budget may increase the profit of ABC. Investigate to what extend the advertising budget can be increased so that it will be beneficial to ABC. Discuss the profit that ABC will gain in this case. (CLO2, 15 Marks) 5. If management decides to increase the total unit production to 603, argue by how much the profit get increased. (CLO2, 10 Marks) 6. Management decided to increase the profit gained from Abu Dhabi dealers by 10 AED, Dubai dealers by 5 AED and Sharjah dealers by 5 AED. Argue on whether the optimal solution remains the same and support your answer with clear justification. Based on your arguments, deduce the new profit of ABC in this case. (CLO2, 15 Marks)
