Exam 14: Applications of Linear Optimization

Use the table below to answer the following question(s). Pickson Luthiers Corporation makes four models of electric guitars, ScarCT, Dela Mort, Warax, and Invazen. Each guitar must flow through five departments, assembly, painting, sound testing, inspection, and packaging. The table below shows the relevant data. Production rates are shown in units/hour. (ScarCT is assembled elsewhere). Pickson wants to determine how many guitars to make to maximize monthly profit. Pickson Luthiers Corporation Data Guitar Model Selling price/Unit Variable cost/Unit Min Sales Max Sales ScarCT 750.00 660.00 0 2500 Dela Mort 788.00 680.00 0 2000 Warax 800.00 700.00 100 1000 Invazen 850.00 800.00 80 500 Production rates (units/hour) ScarCT Dela Mort Warax Invazen Hours Available Assembly - 35 25 20 220 Painting 35 20 15 10 220 Sound Testing 20 10 20 18 220 Inspection 10 12 8 5 220 Packaging 9 10 5 8 220 Use a linear optimization model based on the data to answer the following question. -According to the linear optimization model, what is the total hours spent for painting all the models?

Use the table below to answer the following question(s). The Riviera Transport Company (RTC) produces car accessories at two plants: Dallas and Atlanta. They ship them to major distribution centers in Houston, San Jose, Jacksonville, and Memphis. The accounting, production, and marketing departments have provided the information in the table below, which shows the unit cost of shipping between any plant and distribution center, plant capacities over the next planning period, and distribution center demands. RTC's supply chain manager faces the problem of determining how much to ship between each plant and distribution center to minimize the total transportation cost, not exceed available capacity, and meet customer demand. Assume Xij = amount shipped from plant i to distribution center j, where i = 1 represents Dallas, i = 2 represents Atlanta, j = 1 represents Houston, and so on. Transportation Model Data Distribution Center Plant Houston San Jose Jacksonville Memphis Capacity Dallas 13.00 15.25 10.99 18.48 1250 Atlanta 10.75 15.16 9.65 18.50 750 Demand 175 325 480 950 Answer the following question(s) using a linear optimization model. -According to the transportation model, what is the amount shipped from Atlanta to Memphis?

constraints essentially state that input = output and ensure that the flow of material or money is accounted for at locations or between time periods.

Use the table below to answer the following question(s). Letherin Hides is a company that makes boots specifically targeting college students. Forecasts of sales for the next year are 200 in the summer, 450 in the autumn, and 500 in the winter. Accessories that are used on the boots are purchased from a supplier for $31.66. The cost of capital is estimated to be 24% per year (or 6% per quarter); thus, the holding cost per item is 0.06($31.66) = $1.9 per quarter (rounded figure). Letherin Hides hires freelance art designers at part-time to craft designs during the summer, and they earn $6 per hour. In the autumn, labor is more difficult to keep, and the owner must pay $6.5 per hour to retain qualified help. Because of the high demand for part-time help during the winter holiday season, labor rates are higher in the winter, and workers earn $7.75 per hour. Each boot design takes 2 hours to complete. How should production be planned over the three quarters to minimize the combined production and inventory holding costs? The table below provides information on Letherin Hides boot design cost and production. Letherin Hides Data Summer Autumn Winter Unit Production Cost 12 13 15.5 Unit Inventory Holding Cost 1.9 1.9 1.9 Demand 200 450 500 Use a linear optimization model based on the data to answer the following questions. -According to the linear optimization model, what is the net production for autumn?

Use the table below to answer the following question(s). Pickson Luthiers Corporation makes four models of electric guitars, ScarCT, Dela Mort, Warax, and Invazen. Each guitar must flow through five departments, assembly, painting, sound testing, inspection, and packaging. The table below shows the relevant data. Production rates are shown in units/hour. (ScarCT is assembled elsewhere). Pickson wants to determine how many guitars to make to maximize monthly profit. Pickson Luthiers Corporation Data Guitar Model Selling price/Unit Variable cost/Unit Min Sales Max Sales ScarCT 750.00 660.00 0 2500 Dela Mort 788.00 680.00 0 2000 Warax 800.00 700.00 100 1000 Invazen 850.00 800.00 80 500 Production rates (units/hour) ScarCT Dela Mort Warax Invazen Hours Available Assembly - 35 25 20 220 Painting 35 20 15 10 220 Sound Testing 20 10 20 18 220 Inspection 10 12 8 5 220 Packaging 9 10 5 8 220 Use a linear optimization model based on the data to answer the following question. -According to the linear optimization model, what is the net profit per unit on Dela Mort?

Linear optimization cannot be used on problems having multiple time periods.

Use the table below to answer the following question(s). Pickson Luthiers Corporation makes four models of electric guitars, ScarCT, Dela Mort, Warax, and Invazen. Each guitar must flow through five departments, assembly, painting, sound testing, inspection, and packaging. The table below shows the relevant data. Production rates are shown in units/hour. (ScarCT is assembled elsewhere). Pickson wants to determine how many guitars to make to maximize monthly profit. Pickson Luthiers Corporation Data Guitar Model Selling price/Unit Variable cost/Unit Min Sales Max Sales ScarCT 750.00 660.00 0 2500 Dela Mort 788.00 680.00 0 2000 Warax 800.00 700.00 100 1000 Invazen 850.00 800.00 80 500 Production rates (units/hour) ScarCT Dela Mort Warax Invazen Hours Available Assembly - 35 25 20 220 Painting 35 20 15 10 220 Sound Testing 20 10 20 18 220 Inspection 10 12 8 5 220 Packaging 9 10 5 8 220 Use a linear optimization model based on the data to answer the following question. -According to the linear optimization model, what would be the total time spent on inspecting the Dela Mort models?

Use the table below to answer the following question(s). The Riviera Transport Company (RTC) produces car accessories at two plants: Dallas and Atlanta. They ship them to major distribution centers in Houston, San Jose, Jacksonville, and Memphis. The accounting, production, and marketing departments have provided the information in the table below, which shows the unit cost of shipping between any plant and distribution center, plant capacities over the next planning period, and distribution center demands. RTC's supply chain manager faces the problem of determining how much to ship between each plant and distribution center to minimize the total transportation cost, not exceed available capacity, and meet customer demand. Assume Xij = amount shipped from plant i to distribution center j, where i = 1 represents Dallas, i = 2 represents Atlanta, j = 1 represents Houston, and so on. Transportation Model Data Distribution Center Plant Houston San Jose Jacksonville Memphis Capacity Dallas 13.00 15.25 10.99 18.48 1250 Atlanta 10.75 15.16 9.65 18.50 750 Demand 175 325 480 950 Answer the following question(s) using a linear optimization model. -In a sensitivity report, a solution is considered a(n) solution if the right-hand-side value of any constraint has a zero Allowable Increase or Allowable Decrease.

Use the table below to answer the following question(s). The Riviera Transport Company (RTC) produces car accessories at two plants: Dallas and Atlanta. They ship them to major distribution centers in Houston, San Jose, Jacksonville, and Memphis. The accounting, production, and marketing departments have provided the information in the table below, which shows the unit cost of shipping between any plant and distribution center, plant capacities over the next planning period, and distribution center demands. RTC's supply chain manager faces the problem of determining how much to ship between each plant and distribution center to minimize the total transportation cost, not exceed available capacity, and meet customer demand. Assume Xij = amount shipped from plant i to distribution center j, where i = 1 represents Dallas, i = 2 represents Atlanta, j = 1 represents Houston, and so on. Transportation Model Data Distribution Center Plant Houston San Jose Jacksonville Memphis Capacity Dallas 13.00 15.25 10.99 18.48 1250 Atlanta 10.75 15.16 9.65 18.50 750 Demand 175 325 480 950 Answer the following question(s) using a linear optimization model. -According to the Sensitivity report on the model, by what price should the unit cost of shipment reduce to make shipment from Dallas to Houston feasible?