A company makes two types of sofas, regular and long, at two locations, one in Msamvu and one in Kihonda. The plant in Msamvu has a daily operating budget of Tsh 45,000,000 and can produce at most 300 sofas daily in any combination. It costs Tsh 150,000 to make a regular sofa and Tsh 200,000 to make a long sofa at the Msamvu plant. The Kihonda plant has a daily operating budget of Ksh 36,000,000, can produce at most 250 sofas daily in any combination and makes a regular sofa for Ksh 135,000 and a long sofa for Ksh 180,000. The company wants to limit production to a maximum of 250 regular sofas and 350 long sofas each day. If the company makes a proﬁt of Ksh 50,000 on each regular sofa and Ksh 70,000 on each long sofa, how many of each type should be made at each plant in order to maximize proﬁt? Formulate this problem as an LP mode

A company makes two types of sofas, regular and long, at two locations, one in Msamvu and one in Kihonda. The plant in Msamvu has a daily operating budget of Tsh 45,000,000 and can produce at most 300 sofas daily in any combination. It costs Tsh 150,000 to make a regular sofa and Tsh 200,000 to make a long sofa at the Msamvu plant. The Kihonda plant has a daily operating budget of Ksh 36,000,000, can produce at most 250 sofas daily in any combination and makes a regular sofa for Ksh 135,000 and a long sofa for Ksh 180,000. The company wants to limit production to a maximum of 250 regular sofas and 350 long sofas each day. If the company makes a proﬁt of Ksh 50,000 on each regular sofa and Ksh 70,000 on each long sofa, how many of each type should be made at each plant in order to maximize proﬁt? Formulate this problem as an LP mode

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter11: Simulation Models

Section: Chapter Questions

Problem 69P: The Tinkan Company produces one-pound cans for the Canadian salmon industry. Each year the salmon...

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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.
There is an upstream Picking department that feeds two downstream Packing departments: Pack Singles and Pack Multis. Those Packing departments feed to a Shipping department that loads the outgoing trucks. 40% of your Pick volume goes to Pack Singles and has a packing rate of 104 units per labor hour (uph). 60% of the Pick volume goes to Pack Multis and has a pack rate of 215 units per labor hour. Your pickers pick both Single and Multi items throughout the day at an overall average rate of 114 units per labor hour. All units that are packed in both processes go through the Ship process at a rate of 570 units per hour. You have 102 people today for all 4 departments and you absolutely must pack 47,880 units in Pack Multis Items to meet a customer promise metric. How do you allocate labor to balance the flow in your department if you work a 10 hour shift? Do not assume breaks or lunches in your answer. Redirect 1: You now need to process all of the Pack Singles Volume in the first 5…
Machine A costs Rs 45,000 and its operating costs are estimated to be Rs 1,000 for the first year increasing by Rs 10,000 per year in the second and subsequent years.Machine B costs Rs 50,000 and operating costs are Rs 2,000 for the first year, increasing by Rs 4,000 in the second and subsequent years.If at present we have a machine of type A, should we replace it with B? if so when?Assume that both machines have no resale value and their future costs are not discounted.
The Finishing Department had 5,000 incomplete units in its beginning Work-in-Process Inventory which were 100% complete as to materials and 30% complete as to conversion costs. 15,000 units were received from the previous department. The ending Work-in-Process Inventory consisted of 2,000 units which were 50% complete as to materials and 30% complete as to conversion costs. The Finishing Department uses first-in, first-out (FIFO) process costing.What are the equivalent units of production for the conversion costs during the period? 17,100. 14,500. 15,100. 16,500.
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…
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 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…
Alice, Wonder, and Land are freshmen under the marketing management program. Every month, they purchase a piece of Panda ballpen. The price of the ball pen is Php9.50.According to a recent survey, 45% of the marketing freshmen have the samepurchasing behavior as Alice, Wonder, and Land. Another 30% also purchase Panda ballpens regularly at the same price; however, they purchase once every 2 weeks. There are approximately 280 freshmen under the marketing management program. Assuming that the behavior is consistent throughout their 4-year stay in the program, what is the approximate projected revenue that can be generated from the marketing freshmen for the entire duration of their stay in the program?
Company ZWZ manufactures three products in a serial system; Product XA is manufactured in Stage 1, Product XB in Stage 2, and XC in Stage 3. Product XB has a sales potential in the market; hence, some of it can be sold at the end of Stage 2, and the remaining can be moved to Stage 3. The third stage produces Product XC, and then delivers it to customers. Two units of Product XA produced in Stage 1 are required for each unit of Product XB in Stage 2. In addition, four units of Product XB produced in Stage 2 are required for each unit of Product XC in Stage 3. Stage 1 can only use regular time; however, Stage 2 has the options of using regular time and overtime in manufacturing. On the other hand, Stage 3 has only one alternative, which is subcontracting. The pertinent data are provided below: Stage 2 Stage 1 11 No overtime No subcontracting No sales 0.07 Unit regular time cost (TL) Unit overtime cost (TL) Unit subcontracting cost (TL) Unit selling price (TL) Unit processing time (hrs)…
Fedori Corporation has a Parts Division that does work for other Divisions in the company as well as for outside customers. The company's Machinery Division has asked the Parts Division to provide it with 4,000 special parts each year. The special parts would require P23.00 per unit in variable production costs. The Machinery Division has a bid from an outside supplier for the special parts at P37.00 per unit. In order to have time and space to produce the special part, the Parts Division would have to cut back production of another part-the YR24 that it presently is producing. The YR24 sells for P40.00 per unit, and requires P28.00 per unit in variable production costs. Packaging and shipping costs of the YR24 are P3.00 per unit. Packaging and shipping costs for the new special part would be only P1.50 per unit. The Parts Division is now producing and selling 15,000 units of the YR24 each year. Production and sales of the YR24 would drop by 20% if the new special part is produced for…
We run a fresh produce stand at farmer’s market where we sell avocados and artichokes. Each morning, a supplier drops off bags of these products. We can buy up to 200 bags of avocados and up to 175 bags of artichokes each morning. We resell the bags to customers throughout the day. The contribution margin of avocados is $15/bag; the contribution margin of artichokes is $20/bag. We sell at least twice as many bags of avocados as we do artichokes. We have found that our normal daily demand is between 140 and 350 total bags what are the constaints
a) Suppose you walk into a large supermarket at 2 am with a friend. Your friend says, "I can't believe that these stores stay open all night. Only one out of fifteen checkout lines is open. There can't be more than ten shoppers in this store. It just doesn't make any sense for this store to be open all night." What conditions must be true for it to be to the advantage of the supermarket to stay open all night? b) Your friend has a large garden and grows fresh fruit and vegetables to be sold at a local "farmer's market." Last year your friend was the only worker in the garden, without any additional workers. However, this year your friend hired a worker and production more than doubled. He comments "Next summer, I think I'll hire another two workers (so total workers including myself would go up from 2 to 4) and my output should again more than double". Is it likely that he could hire more workers and always continue to reap greater than proportional increases in production? Why?
Digital Controls, Inc. (DCI), manufactures two models of a radar gun used by police to monitor the speed of automobiles. Model A has an accuracy of plus or minus 1 mile per hour, whereas the smaller model B has an accuracy of plus or minus miles per hour. For the next week, the company has orders for 100 units of model A and 150 units of model B. Although DCI purchases all the electronic components used in both models, the plastic cases for both models are manufactured at a DCI plant in Newark, New Jersey. Each model A case requires 4 minutes of injection-molding time and 6 minutes of assembly time. Each model B case requires 3 minutes of injection-molding time and 8 minutes of assembly time. For next week, the Newark plant has 600 minutes of injection-molding time available and 1,080 minutes of assembly time available. The manufacturing cost is $10 per case for model A and $6 per case for model B. Depending upon demand and the time available at the Newark plant, DCI occasionally…