Question 2: Super Malls Inc. runs a chain of shopping malls across the UK. Recently, Super Malls has purchased a 10,000 sq ft building in central London, and the board is wondering how they should rent out the space in order to maximise profits. The following table presents the different types of shops that have shown an interest in renting space at the mall, together with the required space per shop, the minimum and maximum number of each shop type that Super Malls wants to have at the mall, as well as the anticipated profits that each shop would generate (in 1,000s). [50 marks] Shop type Department Accessories Clothes Book Shoe Space (sq ft) 2.500 600 1,200 900 500 Minimum # 1 0 0 1 0 Maximum # 2 3 3 2 3 Profits 30 8 20 15 10 (a) Assume that Super Malls receives a profit contribution of 3% from each shop at the mall. How many shops of each type should Super Malls have in the mall in order to maximise its profits? Derive an integer Program that solves the problem. Do not solve the problem! [15 marks] (b) Explain how to formulate the following constraints that could be added to the Integer Program in part(a): 1. There should not be both clothes stores and shoe stores. [5 marks] 2. The overall space occupied by the clothes and shoe shops should not exceed 2,000 sq ft [5 marks] 3. If there is a shoe store, then there should be at least one clothes store. [5 marks] (c) Consider again the problem from part (a), but assume now that the profits of each shop depend on the number of shops of that type that are present in the mall: 3 Stores Shop type Department Accessories Clothes Book Shoe 1 Store 30 8 20 15 10 2 Stores 25 7 17 13 9 6 12 8 For example, 1 department store generates 30,000 profits per year and requires 2,500 sq ft of space, whereas 2 department stores generate 2 * 25,000 profits per year and require 2 * 2,500 sq ft of space. How many shops of each type should SuperMalls now rent out to in order to maximise its profits? Derive a Binary Program that solves the problem. Do not solve the problem! [20 marks] Question 2: Super Malls Inc. runs a chain of shopping malls across the UK. Recently, Super Malls has purchased a 10,000 sq ft building in central London, and the board is wondering how they should rent out the space in order to maximise profits. The following table presents the different types of shops that have shown an interest in renting space at the mall, together with the required space per shop, the minimum and maximum number of each shop type that Super Malls wants to have at the mall, as well as the anticipated profits that each shop would generate (in 1,000s). [50 marks] Shop type Department Accessories Clothes Book Shoe Space (sq ft) 2.500 600 1,200 900 500 Minimum # 1 0 0 1 0 Maximum # 2 3 3 2 3 Profits 30 8 20 15 10 (a) Assume that Super Malls receives a profit contribution of 3% from each shop at the mall. How many shops of each type should Super Malls have in the mall in order to maximise its profits? Derive an integer Program that solves the problem. Do not solve the problem! [15 marks] (b) Explain how to formulate the following constraints that could be added to the Integer Program in part(a): 1. There should not be both clothes stores and shoe stores. [5 marks] 2. The overall space occupied by the clothes and shoe shops should not exceed 2,000 sq ft [5 marks] 3. If there is a shoe store, then there should be at least one clothes store. [5 marks] (c) Consider again the problem from part (a), but assume now that the profits of each shop depend on the number of shops of that type that are present in the mall: 3 Stores Shop type Department Accessories Clothes Book Shoe 1 Store 30 8 20 15 10 2 Stores 25 7 17 13 9 6 12 8 For example, 1 department store generates 30,000 profits per year and requires 2,500 sq ft of space, whereas 2 department stores generate 2 * 25,000 profits per year and require 2 * 2,500 sq ft of space. How many shops of each type should SuperMalls now rent out to in order to maximise its profits? Derive a Binary Program that solves the problem. Do not solve the problem! [20 marks]