Question 2. (18 marks] A clothing company produces two different types of shirts: casual shirts, and dress shirts. Each shirt requires some amount of fabric (measured in metres), buttons, and labour (measured in hours). The company has production lines for producing each type of shirt separately. Additionally, the company has determined that it can waste less fabric if it cuts parts for both types of shirts out of the same length of cloth. It has developed a third production line for this method, which costs slightly more labour. The total amount of resources required and the number of shirts produced by using each production line for one day is shown below: Production Fabric Buttons Labour Line Required Required Required 140 210 85 2 125 400 3 200 500 180 1 Casual Shirts Produced 70 0 60 Dress Shirts Produced 0 50 40 75 (a) Suppose that the company has only 1500 metres of fabric, 3500 buttons, and 1800 hours of labour available. It can sell an unlimited number of casual shirts for 45 each and an unlimited number of dress shirts for 65 each. It wants to know the most revenue it can generate using only these available resources. Write a linear program that models this problem (you do not need to solve this program). (10) (b) Now suppose that the company has the same amount of resources available as in part (b), and can still sell any number of casual shirts at a price of 45. However, it has determined that its retailers can sell only up to 250 dress shirts at a price of 65, and then up to 300 additional dress shirts at a discounted sale price of 39. Again, the company wants to know the most revenue it can generate using only its available resources. Write a linear program that models this optimisation problem. [8] Question 2. (18 marks] A clothing company produces two different types of shirts: casual shirts, and dress shirts. Each shirt requires some amount of fabric (measured in metres), buttons, and labour (measured in hours). The company has production lines for producing each type of shirt separately. Additionally, the company has determined that it can waste less fabric if it cuts parts for both types of shirts out of the same length of cloth. It has developed a third production line for this method, which costs slightly more labour. The total amount of resources required and the number of shirts produced by using each production line for one day is shown below: Production Fabric Buttons Labour Line Required Required Required 140 210 85 2 125 400 3 200 500 180 1 Casual Shirts Produced 70 0 60 Dress Shirts Produced 0 50 40 75 (a) Suppose that the company has only 1500 metres of fabric, 3500 buttons, and 1800 hours of labour available. It can sell an unlimited number of casual shirts for 45 each and an unlimited number of dress shirts for 65 each. It wants to know the most revenue it can generate using only these available resources. Write a linear program that models this problem (you do not need to solve this program). (10) (b) Now suppose that the company has the same amount of resources available as in part (b), and can still sell any number of casual shirts at a price of 45. However, it has determined that its retailers can sell only up to 250 dress shirts at a price of 65, and then up to 300 additional dress shirts at a discounted sale price of 39. Again, the company wants to know the most revenue it can generate using only its available resources. Write a linear program that models this optimisation problem. [8]
