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Madonna's Latest Album - Optimisation & Decision Models - Business Analytics Assignment Help
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Madonna's Latest Album Business Analytics Assignment Help
Assignment Task: You have been assigned to arrange the songs on the cassette version of Madonna's latest album. A cassette tape has two sides (side A and side B). The length and type of each song are given in the table below: (a) Formulate an integer linear program that determines an arrangement of the songs such that the songs on each side of the cassette total between 14 and 16 minutes in length. (b) How does the integer linear program from (a) change if each side of the cassette must have exactly two ballads? (c) How does the integer linear program from (a) change if side A of the cassette must have at least three hit songs? (d) How does the integer linear program from (a) change if either song 5 or song 6 (but not both) must be on side A of the cassette (e) If songs 2 and 4 are both on side A, then song 5 must be on side B. How would you change the integer linear program from (a) to reflect this? SuperMalls Inc. runs a chain of shopping malls across the UK. Recently, SuperMalls has purchased a 10,000 sq ft building in central London, and the board is wondering how they should rent out 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 SuperMalls wants to have at the mall, as well as the anticipated profits that each shop would generate (in £1,000s). (a) Assume that SuperMalls receives a profit contribution of 3% from each shop at the mall. How many shops of each type should SuperMalls have in the mall in order to maximise its profits? Derive an Integer Program that solves the problem. Do not solve the problem! (b) Explain how to formulate the following constraints that could be added to the Integer Program in part (a):- The cumulative number of clothes and shoe shops should be between1 and 3.
- The overall space occupied by the clothes and shoe shops should not exceed 2,000 sq ft
- If there is a shoe store, then there should be at least one clothing store.
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