Question 1 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 autumn/winter season of 2020, 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 the Coronavirus pandemic, 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 Variable Final Value Reduced Cost 0 60 144 Objective Coefficient ? ? ? Allowable Increase 46.6 Infinite 10 Allowable Decrease Infinite 29.125 Infinite 0 0 -10 # High Heels # Flats # Hours Overtime/Sewing # Hours Overtime/Polishing 85.2 0 ? 30 157.5 Constraints Constraint Final Value Shadow Price RHS Value 0 ? ? ? Allowable Increase Infinite 85.2 92.5 ? ? ? Allowable Decrease 168 14.8 470 30 25.2 ? 0 ? Infinite 14.8 Sewing Time Polishing Time Leather Availability Overtime Availability Minimum High Heels Minimum Flats ? -46.6 ? 58.75 60 ? 0 ? 94 Infinite (i) Formulate the linear programming (LP) model for Wittner. (7 marks) (ii) For the optimal solution, what is the cost of overtime? (3 marks) (iii) For the optimal solution, if Wittner decides to increase overtime for either sewing or polishing, which one should it choose? Why? (3 marks) Question 1 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 autumn/winter season of 2020, 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 the Coronavirus pandemic, 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 Variable Final Value Reduced Cost 0 60 144 Objective Coefficient ? ? ? Allowable Increase 46.6 Infinite 10 Allowable Decrease Infinite 29.125 Infinite 0 0 -10 # High Heels # Flats # Hours Overtime/Sewing # Hours Overtime/Polishing 85.2 0 ? 30 157.5 Constraints Constraint Final Value Shadow Price RHS Value 0 ? ? ? Allowable Increase Infinite 85.2 92.5 ? ? ? Allowable Decrease 168 14.8 470 30 25.2 ? 0 ? Infinite 14.8 Sewing Time Polishing Time Leather Availability Overtime Availability Minimum High Heels Minimum Flats ? -46.6 ? 58.75 60 ? 0 ? 94 Infinite (i) Formulate the linear programming (LP) model for Wittner. (7 marks) (ii) For the optimal solution, what is the cost of overtime? (3 marks) (iii) For the optimal solution, if Wittner decides to increase overtime for either sewing or polishing, which one should it choose? Why
