If the company wishes to maximize profi t, how many hockey sticks and chess sets should be produced per day?
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We describe the steps involved in solving a simple linear programming model in the context of a sample problem, that of Puck and Pawn Company, which manufactures hockey sticks and chess sets. Each hockey stick yields an incremental profi t of $2, and each chess set, $4. A hockey stick requires 4 hours of processing at machine center A and 2 hours at machine center B. A chess set requires 6 hours at machine center A, 6 hours at machine center B, and 1 hour at machine center C. Machine center A has a maximum of 120 hours of available capacity per day, machine center B has 72 hours, and machine center C has 10 hours. If the company wishes to maximize profi t, how many hockey sticks and chess sets should be produced per day? |
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- Assume the demand for a companys drug Wozac during the current year is 50,000, and assume demand will grow at 5% a year. If the company builds a plant that can produce x units of Wozac per year, it will cost 16x. Each unit of Wozac is sold for 3. Each unit of Wozac produced incurs a variable production cost of 0.20. It costs 0.40 per year to operate a unit of capacity. Determine how large a Wozac plant the company should build to maximize its expected profit over the next 10 years.A company manufactures plastic bottles, buckets, and cups. The profit units are $10 for a plastic bottle, $25 for a bucket,and 58 for a bag of cups. The machine that makes the goods has a capacity of 400 hours each month. The bottle takestwo hours to make, the bucket three hours, and the cup one hour. The company has a total of 890 units of plastic. Plasticbottles require three units, buckets five units, and cups one unit. In addition, there are 200 kg of a novel chemicalcomponent. This unique chemical component is employed in plastic bottles (2 kilogram), buckets (4 kg), and cups (0.5kg) . There is an order to produce only 50 bags of plastic cup. The company wants to find the optimal plan to maximizeprofit. Use the Simplex method to solve this problem.At a small but growing airport, the local airline company is purchasing a new tractor for a tractor-trailer train to bring luggage to and from the airplanes. A new mechanized luggage system will be installed in 3 years, so the tractor will not be needed after that. However, because it will receive heavy use, so that the running and maintenance costs will increase rapidly as the tractor ages, it may still be more economical to replace the tractor after 1 or 2 years. The following table gives the total net discounted cost associated with purchasing a tractor (purchase price minus trade-in allowance, plus running and maintenance costs) at the end of year i and trading it in at the end of year j (where year O is now). i 012 1 $13,000 j 2 $28,000 $17,000 3 $48,000 $33,000 $20,000 The problem is to determine at what times (if any) the tractor should be replaced to minimize the total cost for the tractors over 3 years. (a) Formulate this problem as a minimum cost flow problem by showing the…
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- fi Auto mobile company manufactures cars and trucks. Each vehicle must be processed in the paint shop and body assembly shop. If the paint shop were only painting trucks, then 80 per day could be painted. If the paint shop were only painting cars, then 120 per day could be painted. If the body shop were only producing cars, then it could process 100 per day. If the body shop were only producing trucks, then it could process 100 per day. Each truck contributes GHS60,000 to profit, and each car contributes GHS40,000 to profit. Use linear programming to determine a daily production schedule that will maximize the company’s profits.A manufacturing plant produces a product 'A' that requires one unit of 'B' and ½ unit of 'C'. Each unit of 'B' is comprised of one unit of 'D', two units of 'E', and one unit of 'F'. Each unit of 'C' requires ½ unit of 'G' and three units of 'H'. The manufacturing lead times for the components are as follows: 'A' - two weeks, 'B' - one week, 'C' - two weeks, 'D' - two weeks, 'E' - three weeks, 'F' - one week, 'G' - two weeks, 'H' - one week. There are 20 units in stock for each of these components. 100 units of 'A' are needed for delivery in seven weeks: a) Develop the product structure and indexed bill of materials for the product. b) Create a gross and net requirements plan for the manufacturer of the product.Roedel Electronics produces tablet computer accessories, including integrated keyboard tablet stands that connect a keyboard to a tablet device and hold the device at a preferred angle for easy viewing and typing. Roedel produces two different sizes of integrated keyboard tablet stands, small and large. Each size uses the same keyboard attachment, but the stand consists of two different pieces, a top flap and a vertical stand that differ by size. Thus, a completed integrated keyboard tablet stand consists of three subassemblies that are manufactured by Roedel: a keyboard, a top flap and a vertical stand. Roedel's sales forecast indicates that 7,000 small integrated keyboard tablet stands and 5,000 large integrated keyboard tablet stands will be needed to satisfy demand during the upcoming Christmas season. Because only 500 hours of in-house manufacturing time are available, Roedel is considering purchasing some, or all, of the subassemblies from outside suppliers. If Roedel…
- Roedel Electronics produces tablet computer accessories, including integrated keyboard tablet stands that connect a keyboard to a tablet device and hold the device at a preferred angle for easy viewing and typing. Roedel produces two different sizes of integrated keyboard tablet stands, small and large. Each size uses the same keyboard attachment, but the stand consists of two different pieces, a top flap and a vertical stand that differ by size. Thus, a completed integrated keyboard tablet stand consists of three subassemblies that are manufactured by Roedel: a keyboard, a top flap and a vertical stand. Roedel's sales forecast indicates that 7,000 small integrated keyboard tablet stands and 5,000 large integrated keyboard tablet stands will be needed to satisfy demand during the upcoming Christmas season. Because only 500 hours of in-house manufacturing time are available, Roedel is considering purchasing some, or all, of the subassemblies from outside suppliers. If Roedel…Roedel Electronics produces tablet computer accessories, including integrated keyboard tablet stands that connect a keyboard to a tablet device and hold the device at a preferred angle for easy viewing and typing. Roedel produces two different sizes of integrated keyboard tablet stands, small and large. Each size uses the same keyboard attachment, but the stand consists of two different pieces, a top flap and a vertical stand that differ by size. Thus, a completed integrated keyboard tablet stand consists of three subassemblies that are manufactured by Roedel: a keyboard, a top flap and a vertical stand. Roedel's sales forecast indicates that 7,000 small integrated keyboard tablet stands and 5,000 large integrated keyboard tablet stands will be needed to satisfy demand during the upcoming Christmas season. Because only 500 hours of in-house manufacturing time are available, Roedel is considering purchasing some, or all, of the subassemblies from outside suppliers. If Roedel…A manufacturing cell makes three models of a product – AKC1011, BC0001, and AC0102. The daily demand for the three products are as follows: 200 of AKC1011, 500 BC0001, and 300 of AC0102. Develop a balanced mixed-model sequence that should be repeated throughout the day in order to meet demand.