The Blue Mountain Coffee Shop blends coffee on the premises for its customers. It sells three basicblends in 1-pound bags, Special, Mountain Dark, and Mill Regular. It uses four different types of coffeeto produce the blends Brazilian, mocha, Columbian, and mild. The shop has the following blend reciperequirements:BlendMix RequirementsSelling Price/PoundSpecial At least 40% Columbian, at least 30% mocha$6.50DarkAt least 60% Brazilian, no more than 10% mild5.25Regular No more than 60% mild, at least 30% Brazilian3.75The cost of Brazilian coffee is $2.00 per pound, the cost of mocha is $2.75 per pound, the cost ofColumbian is $2.90 per pound, and the cost of mild is $1.70 per pound. The shop has 110 pounds ofBrazilian coffee, 70 pounds of mocha, 80 pounds of Columbian, and 150 pounds of mild coffee availableper week. The shop wants to know the amount of each blend it should prepare each week to maximizeprofit.Formulate a linear programming model for this problem and the model should include the objectivefunction, decision variables, ratio/ percentage constraints.(

Profit maximization is expressed as a function to compute the profit at various levels of…

Answered: Formulate a linear programming model…

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...

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Tri-County Utilities, Inc., supplies natural gas to customers in a three-county area. The company purchases natural gas from two companies: Southern Gas and Northwest Gas. Demand forecasts for the coming winter season are as follows: Hamilton County, 400 units; Butler County, 200 units; and Clermont County, 300 units. Contracts to provide the following quantities have been written: Southern Gas, 500 units; and Northwest Gas, 400 units. Distribution costs for the counties vary, depending upon the location of the suppliers. The distribution costs per unit (in thousands of dollars) are as follows: a. Develop a network representation of this problem. b. Develop a linear programming model that can be used to determine the plan that will minimize total distribution costs. c. Describe the distribution plan and show the total distribution cost. d. Recent residential and industrial growth in Butler County has the potential for increasing demand by as much as 100 units. Which supplier should…
Tri-County Utilities, Inc., supplies natural gas to customers in a three-county area. The company purchases natural gas from two companies: Southern Gas and Northwest Gas. Demand forecasts for the coming winter season are Hamilton County, 400 units; Butler County, 200 units; and Clermont County, 300 units. Contracts to provide the following quantities have been written: Southern Gas, 500 units; and Northwest Gas, 400 units. Distribution costs for the counties vary, depending upon the location of the suppliers. The distribution costs per unit (in thousands of dollars) are as follows: From To Hamilton Butler Clermont Southern Gas 10 20 15 Northwest Gas 12 15 18 Develop a network representation of this problem. Develop a linear programming model that can be used to determine the plan that will minimize total distribution costs. Describe the distribution plan and show the total distribution cost. (First determine initial transportation cost then use…
Tri-County Utilities, Inc., supplies natural gas to customers in a three-county area. The company purchases natural gas from two companies: Southern Gas and Northwest Gas. Demand forecasts for the coming winter season are as follows: Hamilton County, 400 units; Butler County, 200 units; and Clermont County, 300 units. Contracts to provide the following quantities have been written: Southern Gas, 500 units; and Northwest Gas, 400 units. Distribution costs for the counties vary, depending upon the location of the suppliers. The distribution costs per unit (in thousands of dollars) are as follows.
formulate a linear program Vince Oliver plans to invest P 30,000 in municipal bonds, savings bonds, and treasury bills. He wishes to invest a minimum of P 5,000 in each of the three. If the interest rates are 12% for municipal bonds, 8% for savings bonds, and 10% for treasury bills, how much should he invest in each?
Tri-County Utilities, Inc., supplies natural gas to customers in a three-county area. The company purchases natural gas from two companies: Southern Gas and Northwest Gas. Demand forecasts for the coming winter season are Hamilton County, 400 units; Butler County, 200 units; and Clermont County, 300 units. Contracts to provide the following quantities have been written: Southern Gas, 500 units; and Northern Gas, 400 units. Distribution costs for the counties vary, depending upon the location of the suppliers. The distribution costs per units (in thousands of dollars) are as follows: To From Hamilton Butler Clermont Southern Gas 10 20 15 Northern Gas 12 15 18 What is the optimal function value of this problem? a. 900 units b. $13,600 c. none of the answers proposed apply d. 1,200 units e. $11,900
Unidyde is considering expansion of its Fort Myers plant to produce a new chemical compound. The company is evaluating three different expansion plans: Minor, moderate, or major. They can, of course, also do nothing. Long-term profitability will be a function of future demand growth for the chemical compound. The following payoff table gives the present worth future profitability (in $1,000's) estimated by Unidyde management: Demand Growth for Chemical Compound High Medium Low Do Nothing Minor 140 120 120 Expansion Moderate Major 150 220 -260 250 100 -450 1. What is Unidyde's optimal decision if it wishes to minimize its maximum regret? 2. What is Unidyde's optimal decision if it uses the equal likely criteria? 3. Suppose Unidyde estimates the following probabilities hold for demand growth of the chemical compound: P(High Growth) =.20 P(Medium Growth) = .40 P(Low Growth) What is the most that Unidyde should pay for sample information regarding the compound's future growth? (Hint:…
Pierre-Hadrien is a pastry chef in the Parisian restaurant L'Excuse that serves crois-sants and palmiers for breakfast. Pierre-Hadrien needs to work under the daily prod-ucts' constraints imposed by the restaurant's owner. He sets up a linear optimizationproblem to maximize the restaurant's revenue from the sales of croissants and palmiers.Palmiers are sold for $4 each and croissants for $5 each. (Yes, ok, these should be € but let's pretend a French cafe would accept $ for the sake of this exercise.) We assumethat Pierre-Hadrien can sell all the palmiers and croissants he produces. Croissantsand palmiers' production require various quantities of butter, sugar, our and eggs asspecifed in the table below. Palmiers Croissant Total Supplies per day Butter (g) 200 100 15000 Sugar (g) 200 300 25000 Flour (g) 100 200 17000 Eggs (units) 0.4* 0.6* 35 *Note that eggs are in decimals because pastry chefs typically bake the paste formultiple pastries at once. A paste with 3 eggs…
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PROBLEM 7 Eyewitness News is shown on channel 5 Monday through Friday evenings from 5:00 P.M. to 6:00 P.M. During the hour-long broadcast, 18 minutes are allocated to commercials. The remaining 42 minutes of airtime are allocated to single or multiple time segments for local news and features, national news, sports, and weather. The station has learned through several viewer surveys that viewers do not consistently watch the entire news program; they focus on some segments more closely than others. For example, they tend to pay more attention to the local weather than the national news (because they know they will watch the network news following the local broadcast). As such, the advertising revenues generated for commercials shown during the different broadcast segments are $850 per minute for local news and feature segments, $600 per minute for national news, $750 per minute for sports, and $1,000 per minute for the weather. The production cost for local news is…

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Formulate a linear programming model for this problem and the model should include the objective function, decision variables, ratio/ percentage constraints.(