Question 1 (20 marks) Established by HJ Wittner in 1912, "Wittner" is one of the oldest and most famous Australian shoe brands and is known for high quality and luxury men and women leather shoes. For the upcoming autumn/winter season, Wittner has developed new designs for high heels and flat women boots. The two major operations needed to make the boots are sewing and polishing the leather. For each pair of high heel boots, sewing takes 1 hour, polishing takes 1.5 hours and 8 ounces of leather is required. For each pair of flat boots, sewing takes 0.5 hour, polishing takes 0.8 hour and 5 ounces of leather is required. The estimated profit per each pair of high heel boots and flat boots sold are $200 and $150 respectively. Due to some unforeseen circumstances, Wittner is behind schedule to prepare the shoes for the upcoming season across all their stores in Australia and therefore the management is deciding about whether they should have overtime sewing and polishing operations. For one of their stores in Melbourne Central, they have estimated that each hour of overtime for sewing will cost $10 and each hour of overtime for polishing will cost $30. The overtime cannot exceed 100 hours for this store. The available time for sewing and polishing are 300 hours and 120 hours, respectively. The amount of leather available is 1200 ounces. To meet customer demand for this store, Wittner has forecasted the minimum demand for high heel boots and flat boots are 60 and 50 pairs, respectively. Wittner is aiming at maximising its profit from selling high heel and flat boots in their Melbourne Central store. Below is how Wittner's business analyst has solved the LP problem: Variable Cells Constraints i. Formulate the linear programming (LP) model for Wittner. (7 marks) ii. For the optimal solution, what is the cost of overtime? (2 marks) iii. For the optimal solution, if Wittner decides to increase overtime for either sewing or polishing, which one should it choose? Why? (2 marks) iv. For the optimal solution, if Wittner decides to increase the price of high heels by $40 (considering that all costs remain the same), how will the optimal solution and profit change? (2 marks) v. Without changing the optimal solution, what is the lower bound (the minimum value) for profit? (2 marks) vi. Wittner's new forecasts show the minimum demand for high heels might increase by 20%. If they take this increase into account, how much will their profit change? (2 marks) vii. How will the profit change if Wittner reduces the available polishing time by 20 hours and the LP problem is still solvable? (3 marks) Question 1 (20 marks) Established by HJ Wittner in 1912, "Wittner" is one of the oldest and most famous Australian shoe brands and is known for high quality and luxury men and women leather shoes. For the upcoming autumn/winter season, Wittner has developed new designs for high heels and flat women boots. The two major operations needed to make the boots are sewing and polishing the leather. For each pair of high heel boots, sewing takes 1 hour, polishing takes 1.5 hours and 8 ounces of leather is required. For each pair of flat boots, sewing takes 0.5 hour, polishing takes 0.8 hour and 5 ounces of leather is required. The estimated profit per each pair of high heel boots and flat boots sold are $200 and $150 respectively. Due to some unforeseen circumstances, Wittner is behind schedule to prepare the shoes for the upcoming season across all their stores in Australia and therefore the management is deciding about whether they should have overtime sewing and polishing operations. For one of their stores in Melbourne Central, they have estimated that each hour of overtime for sewing will cost $10 and each hour of overtime for polishing will cost $30. The overtime cannot exceed 100 hours for this store. The available time for sewing and polishing are 300 hours and 120 hours, respectively. The amount of leather available is 1200 ounces. To meet customer demand for this store, Wittner has forecasted the minimum demand for high heel boots and flat boots are 60 and 50 pairs, respectively. Wittner is aiming at maximising its profit from selling high heel and flat boots in their Melbourne Central store. Below is how Wittner's business analyst has solved the LP problem: Variable Cells Constraints i. Formulate the linear programming (LP) model for Wittner. (7 marks) ii. For the optimal solution, what is the cost of overtime? (2 marks) iii. For the optimal solution, if Wittner decides to increase overtime for either sewing or polishing, which one should it choose? Why? (2 marks) iv. For the optimal solution, if Wittner decides to increase the price of high heels by $40 (considering that all costs remain the same), how will the optimal solution and profit change? (2 marks) v. Without changing the optimal solution, what is the lower bound (the minimum value) for profit? (2 marks) vi. Wittner's new forecasts show the minimum demand for high heels might increase by 20%. If they take this increase into account, how much will their profit change? (2 marks) vii. How will the profit change if Wittner reduces the available polishing time by 20 hours and the LP problem is still solvable