Please help with constraints. Question provided below with data. Not sure why the dummy constraint is incorrect. (ii) linear programming formulationLet Xj= number of units i shipped to client j, using the indices from the given table. (It may be necessary to combine plants or distributors in a single node in order to solve this problem. Use index number 5 for this type of node. Enter "DNE" in any unusedanswer blanks.)32x11+34x12+ 32x13+ 40x14+ 34x21 + 30x22 + 28x23+ 38x24Маxs.t.+x,+Orders from Clifton Springs X11 †*12 + *13 x14< 5000+++3000Orders from Danville X21 X22 † *23 † 24Orders from/for Dummy Node X31 † X32 † X33 + X34 < 4000Orders for D, X11+x21 < 2000Orders for D, X12+x22< 5000Orders for D3 X13 +x23 < 3000Orders for D4 *14+ x24 < 2000Xj 2 0 for all i, j. Klein Chemicals, Inc., produces a special oil-based material that is currently in short supply. Four of Klein's customers have already placed orders that together exceed the combined capacity of Klein's two plants. Klein's management faces the problem of deciding how manyunits it should supply to each customer. Because the four customers are in different industries, different prices can be charged because of the various industry pricing structures. However, slightly different production costs at the two plants and varying transportation costsbetween the plants and customers make a "sell to the highest bidder" strategy unacceptable. After considering price, production costs, and transportation costs, Klein established the following profit per unit for each plant-customer alternative.CustomerPlant31D21D3D4Clifton Springs$32$34$32$40Danville$34$30$28$38The plant capacities and customer orders are as follows.PlantCapacity (units)Distributor Orders (units)Clifton Springs5,000D12,000Danville3,000D25,000D33,000D42,000

(H) linear programming formulation Let x- number of units i shipped to client j, using the indices from the given table. (It may be necessary to combine plants or distributors in a single node in order to solve this problem. Use index number 5 for this type of node. Enter "DNE" in any unused answer blanks.) Max 32r1 +34x,2 + 32r13 + 40x14 + 34x21 + 30x + 28x + 38x24 s.t. Orders from Clifton Springs X11 +x12 +x13+x14 < 5000 Orders from Danville X21 +X22 +x23 + X24S3000 Orders from/for Dummy Node X3I +x32 + x33 +x34S 4000 Orders for D, Xu +x21 S 2000 Orders for D, X12 +X22S 5000 Orders for D, X13 + X23 < 3000 Orders for D. X14 +x24S 2000 Xy 2 0 for all 1, j.

(H) linear programming formulation Let x- number of units i shipped to client j, using the indices from the given table. (It may be necessary to combine plants or distributors in a single node in order to solve this problem. Use index number 5 for this type of node. Enter "DNE" in any unused answer blanks.) Max 32r1 +34x,2 + 32r13 + 40x14 + 34x21 + 30x + 28x + 38x24 s.t. Orders from Clifton Springs X11 +x12 +x13+x14 < 5000 Orders from Danville X21 +X22 +x23 + X24S3000 Orders from/for Dummy Node X3I +x32 + x33 +x34S 4000 Orders for D, Xu +x21 S 2000 Orders for D, X12 +X22S 5000 Orders for D, X13 + X23 < 3000 Orders for D. X14 +x24S 2000 Xy 2 0 for all 1, j.

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter2: Introduction To Spreadsheet Modeling

Section: Chapter Questions

Problem 20P: Julie James is opening a lemonade stand. She believes the fixed cost per week of running the stand...

See similar textbooks

Similar questions

Klein Chemicals, Inc., produces a special oil-based material that is currently in short supply. Four of Klein's customers have already placed orders that together exceed the combined capacity of Klein's two plants. Klein's management faces the problem of deciding how many units it should supply to each customer. Because the four customers are in different industries, different prices can be charged because of the various industry pricing structures. However, slightly different production costs at the two plants and varying transportation costs between the plants and customers make a "sell to the highest bidder" strategy unacceptable. After considering price, production costs, and transportation costs, Klein established the following profit per unit for each plant-customer alternative. Plant Customer D1    1 D2    2 D3    3 D4    4 Clifton Springs    1 $32 $34 $32 $40 Danville    2 $34 $30 $28 $38 The plant capacities and customer orders are as follows. Plant Capacity…
Klein Chemicals, Inc., produces a special oil-based material that is currently in short supply. Four of Klein's customers have already placed orders that together exceed the combined capacity of Klein's two plants. Klein's management faces the problem of deciding how many units it should supply to each customer. Because the four customers are in different industries, different prices can be charged because of the various industry pricing structures. However, slightly different production costs at the two plants and varying transportation costs between the plants and customers make a "sell to the highest bidder" strategy unacceptable. After considering price, production costs, and transportation costs, Klein established the following profit per unit for each plant-customer alternative. Plant Customer D1    1 D2    2 D3    3 D4    4 Clifton Springs    1 $32 $34 $32 $40 Danville    2 $34 $30 $28 $38 The plant capacities and customer orders are as follows. Plant Capacity…
Klein Chemicals, Inc’, produces a special oil-based material that is currently in short supply. Four of Klein’s customers have already placed orders that together exceed the combined capacity of Klein’s two plants. Klein’s management faces the problem of deciding how many units it should supply to each customer. Because the four customers are in different industries, different prices can be charged because of the various industry pricing structures. However, slightly different production costs at the two plants and varying transportation costs between the plants and customers make a “sell to the highest bidder” strategy unacceptable. After considering price, production costs, Klein established the following profit per unit for each plant-customer alternative: Customer Plant                      D1                   D2                    D3                    D4 Clifton Springs     $32                  $34                  $32                  $40      Danville                $34…
The Camera Shop sells two popular models of digital SLR cameras (Camera A Price: 220, Camera B Price: 310). The sales of these products are not independent of each other, but rather if the price of one increase, the sales of the other will increase. In economics, these two camera models are called substitutable products. The store wishes to establish a pricing policy to maximize revenue from these products. A study of price and sales data shows the following relationships between the quantity sold (N) and prices (P) of each model: NA = 196 - 0.5PA + 0.35PB NB = 301 + 0.06PA - 0.6PB Construct a model for the total revenue and implement it on a spreadsheet. Develop a two-way data table to estimate the optimal prices for each product in order to maximize the total revenue. Vary each price from $250 to $500 in increments of $10. Max profit occurs at Camera A price of $ . Max profit occurs at Camera B price of $ . Check My Work (3 remaining)
The Sanders Garden Shop mixes two types of grass seed into a blend. Each type of grass has been rated (per pound) according to its shade tolerance, ability to stand up to traffic, and drought resistance, as shown in the table. Type A seed costs $1 and Type B seed costs $2. If the blend needs to score at least 300 points for shade tolerance, 400 points for traffic resistance, and 750 points for drought resistance, how many pounds of each seed should be in the blend? Type A Type B Shade Tolerance 1 1 Traffic Resistance 2 1 Drought Resistance 2 5 Formulate a LP Model for this problem.
Despite of the price increase A Diesel engine uses the following: Type A filter and high-grade lubricating oil costing P10.50 per liter. With this filter, the oil and the filter must be changed every 200 hours of operation, and 5 liters of oil must be added every 50 hours. This filter costs P150 a piece. Eighty liters of oil fill the the engine. Another type, filter B, costing P110 may be used with a lower grade of oil costing P5.50 per liter. However, if this filter is used, the oil and filter must be changed every 250 hours, and 10 liters are added after each 100 hours the engine is used. Which type of filter and oil would you recommend?
Romans Food Market, located in Saratoga, New York, carries a variety of specialty foods from around the world. Two of the store’s leading products use the Romans Food Market name: Romans Regular Coffee and Romans DeCaf Coffee. These coffees are blends of Brazilian Natural and Colombian Mild coffee beans, which are purchased from a distributor located in New York City. Because Romans purchases large quantities, the coffee beans may be purchased on an as-needed basis for a price 12% higher than the market price the distributor pays for the beans. The current market price is $0.45 per pound for Brazilian Natural and $0.67 per pound for Colombian Mild. The compositions of each coffee blend are as follows: Blend Bean Regular DeCaf Brazilian Natural 60% 40% Colombian Mild 40% 60% Romans sells the Regular blend for $3.3 per pound and the DeCaf blend for $4.5 per pound. Romans would like to place an order for the Brazilian and Colombian coffee beans that will enable the…
A manager must make a decision on shipping. There are two shippers, A and B. Both offer a twoday rate: A for $500 and B for $525. In addition, A offers a three-day rate of $460 and a nine-dayrate of $400, and B offers a four-day rate of $450 and a seven-day rate of $410. Annual holdingcosts are 35 percent of unit price. Three hundred boxes are to be shipped, and each box has a priceof $140. Which shipping alternative would you recommend? Explain.
Eastern Chemicals produces two types of lubricating fluids used in industrial manufacturing. Both products cost Eastern Chemicals $1 per gallon to produce. Based on an analysis of current inventory levels and outstanding orders for the next month, Eastern Chemicals’ management specified that at least 30 gallons of product 1 and at least 20 gallons of product 2 must be produced during the next two weeks. Management also stated that an existing inventory of highly perishable raw material required in the production of both fluids must be used within the next two weeks. The current inventory of the perishable raw material is 80 pounds. Although more of this raw material can be ordered if necessary, any of the current inventory that is not used within the next two weeks will spoil—hence, the management requirement that at least 80 pounds be used in the next two weeks. Furthermore, it is known that product 1 requires 1 pound of this perishable raw material per gallon and product 2 requires 2…
Eastern Chemicals produces two types of lubricating fluids used in industrial manufacturing. Both products cost Eastern Chemicals $1 per gallon to produce. Based on an analysis of current inventory levels and outstanding orders for the next month, Eastern Chemicals’ management specified that at least 30 gallons of product 1 and at least 20 gallons of product 2 must be produced during the next two weeks. Management also stated that an existing inventory of highly perishable raw material required in the production of both fluids must be used within the next two weeks. The current inventory of the perishable raw material is 80 pounds. Although more of this raw material can be ordered if necessary, any of the current inventory that is not used within the next two weeks will spoil—hence, the management requirement that at least 80 pounds be used in the next two weeks. Furthermore, it is known that product 1 requires 1 pound of this perishable raw material per gallon and product 2 requires 2…
The Sanders Garden Shop mixes two types of grass seed into a blend. Each type of grass has been rated (per pound) according to its shade tolerance, ability to stand up to traffic, and drought resistance, as shown in the table. Type A seed costs $1 and Type B seed costs $2. If the blend needs to score at least 300 points for shade tolerance, 400 points for traffic resistance, and 750 points for drought resistance, how many pounds of each seed should be in the blend to meet the specifications at minimal cost. How much will the blend cost?Type A Type BShade Tolerance 1 1Traffic Resistance 2 1Drought Resistance 2 5
Markus, Inc., has harvested 400 tons of lumber from a pine forest located outside of Manchester, 200 tons from a forest near Seattle, and 150 tons from a forest outside of Portland. Japan has placed an order for 300 tons at a price of $1200 per ton, Taiwan needs 300 tons and will pay $1000 per ton, and Singapore wants 250 tons at $1000 per ton. It costs Markus, Inc. $500 to get each ton from the pine forest to the port in Manchester, $400 per ton to the port in Seattle, and $300 per ton to Portland. Assume that each pine forest only supplies its closest port. The following table provides the cost for shipping each ton by sea from these ports to the respective countries: ________________________________________________________________________ SHIPPING COST ($/TON) OF LUMBER BY SEA TO: FROM JAPAN TAIWAN SINGAPORE Manchester 250 250 200 Seattle 250 200 200 Portland…