A company produces two products that are processed on two assembly lines. Assembly line 1 has 100 available hours, and assembly line 2 has 42 available hours. Each product requires 10 hours of processing time on line 1, while on line 2 product 1 requires 7 hours and product 2 requires 3 hours. The profit for product 1 is $6 per unit, and the profit for product 2 is $4 per unit. a. Formulate a lincar programming model for this problem. b. Solve this model by using graphical analysis.
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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.The Tinkan Company produces one-pound cans for the Canadian salmon industry. Each year the salmon spawn during a 24-hour period and must be canned immediately. Tinkan has the following agreement with the salmon industry. The company can deliver as many cans as it chooses. Then the salmon are caught. For each can by which Tinkan falls short of the salmon industrys needs, the company pays the industry a 2 penalty. Cans cost Tinkan 1 to produce and are sold by Tinkan for 2 per can. If any cans are left over, they are returned to Tinkan and the company reimburses the industry 2 for each extra can. These extra cans are put in storage for next year. Each year a can is held in storage, a carrying cost equal to 20% of the cans production cost is incurred. It is well known that the number of salmon harvested during a year is strongly related to the number of salmon harvested the previous year. In fact, using past data, Tinkan estimates that the harvest size in year t, Ht (measured in the number of cans required), is related to the harvest size in the previous year, Ht1, by the equation Ht = Ht1et where et is normally distributed with mean 1.02 and standard deviation 0.10. Tinkan plans to use the following production strategy. For some value of x, it produces enough cans at the beginning of year t to bring its inventory up to x+Ht, where Ht is the predicted harvest size in year t. Then it delivers these cans to the salmon industry. For example, if it uses x = 100,000, the predicted harvest size is 500,000 cans, and 80,000 cans are already in inventory, then Tinkan produces and delivers 520,000 cans. Given that the harvest size for the previous year was 550,000 cans, use simulation to help Tinkan develop a production strategy that maximizes its expected profit over the next 20 years. Assume that the company begins year 1 with an initial inventory of 300,000 cans.4) The making of rivet holes in structural steel members can be done by 2 methods. The first method consists of laying out the position of the holes in the members and using a drill press costing P100k. The machinist is paid P60 per hour and he can drill 80 holes per hour. The second method makes use of a multiple-punch machine costing P80k. The punch operator is paid P40 an hour and he can punch out 1 hole for 3 seconds. This method also requires an expense of P1.25 per hole to set the machine. (a) if all other costs are assumed equal, what is the total cost for each machine for 10k holes, assuming the total cost of each machine to be charged to these holes? (b) for how many holes will the costs be equal?
- 1. A manufacturing company is engaged in producing three types of products: X, Y and Z. The production department produces, each day, components sufficient to make 50 units of X, 25 units of Y and 30 units of Z. The management is confronted with the problem of optimizing the daily production of the products in the assembly department, where only 100-man-hours are available daily for assembling the products. The following additional information is available Type of Product Profit Contribution Assembly Time per Product (Hrs) per Units of Products (in PhP) 120 0.8 Y 200 1.7 450 2.5 The company has a daily order commitment for 20 units of product X and a total of 15 units of products Y and Z. Formulate this problem as an LP model so as to maximize the total profit. Using simplex method, find the number of units of product X, Y and Z to product to maximize total profit.A manufacturing firm has four plants and wants to find the most efficient means of meeting the requirements of its four customers. The relevant information for the plants and customers, along with shipping costs in dollars per unit, are shown in the table below: Customer (requirement) Factory (capacity) Customer 1 (125) Customer 2 (150) Customer 3 (175) Customer 4 (75) A (100) $ 15 $ 10 $ 20 $ 17 B (75) $ 20 $ 12 $ 19 $ 20 C (100) $ 22 $ 20 $ 25 $ 14 D (250) $ 21 $ 15 $ 28 $ 12 How many arcs will the network have?A manufacturing firm has four plants and wants to find the most efficient means of meeting the requirements of its four customers. The relevant information for the plants and customers, along with shipping costs in dollars per unit, are shown in the table below: Customer (requirement) Factory (capacity) Customer 1 (125) Customer 2 (150) Customer 3 (175) Customer 4 (75) A (100) $ 15 $ 10 $ 20 $ 17 B (75) $ 20 $ 12 $ 19 $ 20 C (100) $ 22 $ 20 $ 25 $ 14 D (250) $ 21 $ 15 $ 28 $ 12 How many supply nodes are present in this problem? Multiple Choice: 4 3 1 8 16
- A manufacturing firm has four plants and wants to find the most efficient means of meeting the requirements of its four customers. The relevant information for the plants and customers, along with shipping costs in dollars per unit, are shown in the table below: Customer (requirement) Factory (capacity) Customer 1 (125) Customer 2 (150) Customer 3 (175) Customer 4 (75) A (100) $ 15 $ 10 $ 20 $ 17 B (75) $ 20 $ 12 $ 19 $ 20 C (100) $ 22 $ 20 $ 25 $ 14 D (250) $ 21 $ 15 $ 28 $ 12 Note: This question requires Solver.Formulate the problem in Solver and find the optimal solution. What is the optimal quantity to ship from Factory B to Customer 3? Multiple Choice 25 units 50 units 75 units 100 units 125 unitsPlease show how to solve bAn industrial system has two industries with the following input requirements. (a) To roduce $1.00 worth of output, Industry A requires $0.20 of its own products and $0.50 of industry B's products. (b) To produce $1.00 worth of output, industry B requires $0.40 of its own product and $0.30 of industry A's product. Find D, the input-output matrix for this system. D = ? Solve for the output matrix X in the equation X = DX + E where E is the external demand matrix E= [10,000] [20,000] (Round to the nearest whole number.)
- 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…. A group of students organizes a bake sale in which they sell hundreds of cookies at $1per piece. They set up a table on campus and wait for students to come and purchasetheir cookies. Consider the following variables in this bake sale operation:1. Size of the cookies2. Weather conditions on campus3. Organization of the table4. Number of cookies sold5. Competition from other fund-raisers coinciding on campus6. Amount of advertising and shouting of the students at the bake sale table7. Number of students on campus that dayWhich of these variables is an output variable?a. 3b. 4c. 5d. None of the aboveAt 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 B 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 shortest-path problem by drawing a…