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 combinedcapacity 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 betweenthe plants and customers make a "sell to the highest bidder" strategy unacceptable. After considering price, production costs, and transportation costs, Klein established the followingprofit per unit for each plant-customer alternative.PlantClifton SpringsDanvillePlantClifton Springs2DanvilleD₁D3D₂$32 $34 $32 $40$38$34 $30 $28The plant capacities and customer orders are as follows.CustomerCapacity (units)5,0003,000344Distributor Orders (units)D1D₂D3D42,0005,0003,0002,000 (ii) linear programming formulationLetXij; = 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 solvethis problem. Use index number 5 for this type of node. Enter "DNE" in any unused answer blanks.)Maxs.t.Orders from Clifton SpringsOrders from DanvilleOrders from/for Dummy NodeOrders for D₁Orders for D2Orders for D3Orders for D4Xij ≥ 0 for all i, j.

Linear programming is a mathematical technique that is also used in operations management…

Answered: (ii) linear programming formulation Let…

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter7: Nonlinear Optimization Models

Section7.3: Pricing Models

Problem 14P: PRICING SUITS AT SULLIVANS Sullivans is a retailer of upscale mens clothing. Suits cost Sullivans...

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PRICING SUITS AT SULLIVANS Sullivans is a retailer of upscale mens clothing. Suits cost Sullivans 320. The current price of suits to customers is 350. which leads to annual sales of 300 suits. The elasticity of the demand for mens suits is estimated to be 2.5 and assumed to be constant over the relevant price range. Each purchase of a suit leads to an average of 2.0 shirts and 1.5 ties being sold. Each shirt contributes 25 to profit, and each tie contributes 15 to profit. Determine a profit-maximizing price for suits. In the complementary-product pricing model in Example 7.3, we have assumed that the profit per unit from shirts and ties is given. Presumably this is because the prices of these products have already been set. Change the model so that the company must determine the prices of shirts and ties, as well the price of suits. Assume that the unit costs of shirts and ties are, respectively, 20 and 15. Continue to assume that, on average, 2.0 shirts and 1.5 ties are sold along with every suit (regardless of the prices of shirts and ties), but that shirts and ties have their own separate demand functions. These demands are for shirts and ties purchased separately from suit purchases. Assume constant elasticity demand functions for shirts and ties with parameters 288,500 and 1.7 (shirts), and 75,460 and 1.6 (ties). Assume the same unit cost and demand function for suits as in Example 7.3. a. How much should the company charge for suits, shirts, and ties to maximize the profit from all three products? b. The assumption that customers will always buy, on average, the same number of shirts and ties per suit purchase, regardless of the prices of shirts and ties, is not very realistic. How might you change this assumption, and change your model from part a accordingly, to make it more realistic?
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)
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.
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?
A purchasing agent for a particular type of silicon wafer used in the production ofsemiconductors must decide among three sources. Source A will sell the siliconwafers for $2.50 per wafer, independently of the number of wafers ordered. Source Bwill sell the wafers for $2.40 each but will not consider an order for fewer than3,000 wafers, and Source C will sell the wafers for $2.30 each but will not acceptan order for fewer than 4,000 wafers. Assume an order setup cost of $100 and anannual requirement of 20,000 wafers. Assume a 20 percent annual interest rate forholding cost calculations.c. If the replenishment lead time for wafers is three months, determine the reorderpoint based on the on-hand level of inventory of wafers
A purchasing agent for a particular type of silicon wafer used in the production ofsemiconductors must decide among three sources. Source A will sell the siliconwafers for $2.50 per wafer, independently of the number of wafers ordered. Source Bwill sell the wafers for $2.40 each but will not consider an order for fewer than3,000 wafers, and Source C will sell the wafers for $2.30 each but will not acceptan order for fewer than 4,000 wafers. Assume an order setup cost of $100 and anannual requirement of 20,000 wafers. Assume a 20 percent annual interest rate forholding cost calculations.b. What is the optimal value of the holding and setup costs for wafers when theoptimal source is used?
A purchasing agent for a particular type of silicon wafer used in the production ofsemiconductors must decide among three sources. Source A will sell the siliconwafers for $2.50 per wafer, independently of the number of wafers ordered. Source Bwill sell the wafers for $2.40 each but will not consider an order for fewer than3,000 wafers, and Source C will sell the wafers for $2.30 each but will not acceptan order for fewer than 4,000 wafers. Assume an order setup cost of $100 and anannual requirement of 20,000 wafers. Assume a 20 percent annual interest rate forholding cost calculations.a. Which source should be used, and what is the size of the standing order?
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…

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