Question 1: Cheese Cutting (12 marks) Logan Road Creameries wishes to enter the boutique cheesema...
Question 1: Cheese Cutting (12 marks) Logan Road Creameries wishes to enter the boutique cheesemaking industry. As a trial, they have produced a batch of premium cheese to give away (for free) in various supermarkets around Auckland. Cheese is produced in blocks of 13cm in length, but SnackThings-operated supermarkets require 200 cheese blocks of length 4cm, and Woolies-operated supermarkets require 350 cheese blocks of length 3cm. You may assume the height and width of blocks are already appropriate, and that only whole numbers of cheese blocks can be produced. Each 13cm block of cheese costs Logan Road Creameries $2 per block to produce. Excess 3cm blocks (above requirements) can be sold to the supermarkets at 30¢ per block, and excess 4cm blocks can be sold at 50e per block. You may assume that all excess blocks are sold. Due to a lack of machine parts, only 150 cheese blocks at most can be cut using patterns that generate 3 or more 3cm blocks Further, offcuts (i.e. blocks of cheese that are not 3cm or 4cm in length) can be sold to the Proudman Palmer conglomerate for production into 'American cheese food product' at 15c per cm of cheese. Again, you may assume that all offcuts are sold. Logan Road Creameries would like to minimise the net cost (i.e. cost minus any income) of producing and selling the cheese (a) Determine all the sensible combinations for cutting the 13cm cheese blocks into smaller blocks, and state the amount of offcuts in each combination. Do not include combinations that can have another useful length of cheese cut from the remainder. Present these combinations in tabular form, with a row for each combination Hint: Remember to consider the offcuts (b) Formulate the problem described above as an integer program. Remember to define your variables and clearly stat e your objective function and constraints. (c) Enter the problem of part (b) into Excel and solve it to optimality (i.e. using a zero tolerance). Your spreadsheet layout should follow that for a standard linear program as given on pages 3.17 and 3.27 of the workbook. Hand in two printouts or screenshots of the resulting Excel spreadsheet, one showing values and the other showing formulae (d) Give a brief (1-2 sentences) non-technical explanation of your solution to Logan Road Creameries.
Question 1: Cheese Cutting (12 marks) Logan Road Creameries wishes to enter the boutique cheesemaking industry. As a trial, they have produced a batch of premium cheese to give away (for free) in various supermarkets around Auckland. Cheese is produced in blocks of 13cm in length, but SnackThings-operated supermarkets require 200 cheese blocks of length 4cm, and Woolies-operated supermarkets require 350 cheese blocks of length 3cm. You may assume the height and width of blocks are already appropriate, and that only whole numbers of cheese blocks can be produced. Each 13cm block of cheese costs Logan Road Creameries $2 per block to produce. Excess 3cm blocks (above requirements) can be sold to the supermarkets at 30¢ per block, and excess 4cm blocks can be sold at 50e per block. You may assume that all excess blocks are sold. Due to a lack of machine parts, only 150 cheese blocks at most can be cut using patterns that generate 3 or more 3cm blocks Further, offcuts (i.e. blocks of cheese that are not 3cm or 4cm in length) can be sold to the Proudman Palmer conglomerate for production into 'American cheese food product' at 15c per cm of cheese. Again, you may assume that all offcuts are sold. Logan Road Creameries would like to minimise the net cost (i.e. cost minus any income) of producing and selling the cheese (a) Determine all the sensible combinations for cutting the 13cm cheese blocks into smaller blocks, and state the amount of offcuts in each combination. Do not include combinations that can have another useful length of cheese cut from the remainder. Present these combinations in tabular form, with a row for each combination Hint: Remember to consider the offcuts (b) Formulate the problem described above as an integer program. Remember to define your variables and clearly stat e your objective function and constraints. (c) Enter the problem of part (b) into Excel and solve it to optimality (i.e. using a zero tolerance). Your spreadsheet layout should follow that for a standard linear program as given on pages 3.17 and 3.27 of the workbook. Hand in two printouts or screenshots of the resulting Excel spreadsheet, one showing values and the other showing formulae (d) Give a brief (1-2 sentences) non-technical explanation of your solution to Logan Road Creameries.