you are given the following data for a linear programming problem where theobjective is to minimize the cost of conducting two nonnegativeactivities so as to achievethree benefits that do not fall below their minimum levels.Benefit Contribution perUnit of Each ActivityMinimumAcceptableLevelBenefitActivity 1Activity 2156022303126Unit cost$60$50(a) Formulate a linear programming model for this problem.(b) Use the graphical method to solve this model.I am confused with the sensitivity analysis part:(c) What is the sensitivity range of the unit cost of activity 1? Please calculate the optimalobjective value if we change the unit cost of activity 1to 80. What if we change the unitcost of activity 1 to 90? (Hint: You can use excel or python to solve the problem.)(d) What is the sensitivity range of the minimum acceptable level of benefit 3? Pleasecalculate the optimal objective value if change theminimum acceptable level of benefit 3 to 130. What if we change the minimum acceptable level of benefit 3 to 110?(e) What is the sensitivity range of the unit cost of activity 2?Suppose we change the unitcost of the two activities to 90for activity 1 and 80for activity 2. Are the new unit costs in the sensitivity range?Does the optimal solution change? Is the sensitivity rangeapplicable when multiple parameters change?

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Answered: you are given the following data for a…

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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GreenLawns provides a lawn fertilizer and weed control service. The company is adding a special aeration treatment as a low-cost extra service option, which it hopes will help attract new customers. Management is planning to promote this new service in two media: radio and direct-mail advertising. A media budget of $2,500 is available for this promotional campaign. Based on past experience in promoting its other services, GreenLawns obtained the following estimate of the relationship between sales and the amount spent on promotion in these two media. S = −2R2 − 10M2 − 8RM + 18R + 34M where S = total sales in thousands of dollars R = thousands of dollars spent on radio advertising M = thousands of dollars spent on direct-mail advertising. GreenLawns would like to develop a promotional strategy that will lead to maximum sales subject to the restriction provided by the media budget. (a) What is the value of sales (in dollars) if $1,500 is spent on radio advertising and $1,000 is…
Demand is forecasted using the following regression equation: D = 100 + 15(t) where “t” is a specified future time period. The current time period is 0 (t=0). The machines used to make this product have a capacity of 50 units/time period. The company currently has 4 machines yielding a total capacity of 200 units/time period. Due to technology changes, the current equipment will become obsolete at the end of period 15. If a new machine costs $2000, and the net revenue earned per unit is $10, how many machines should be added between today (t=0) and the end of period 15?
Two firms, A and B, each currently dump 168 tons of chemicals into the local river. The government has decided to reduce the pollution and from now on will require a pollution permit for each ton of pollution dumped into the river. The government gives each firm 90 pollution permits. The abatement costs of one ton of pulltion is $122 for Firm A and $147 for Firm B. What would be the total cost of reducing pollution, if the government does NOT allow the firm to trade the permits between each other?
Problem 2 Suppose that for years East Campus' short-run Phillips Curve was such that each 1 percentage point increase in its unemployment rate was associated with a 2-percentage point decline in its inflation rate. Then, during several recent years, the short-run pattern changed such that its inflation rate rose by 3 percentage points for every 1 percentage point drop in its unemployment rate. Graphically, did East Campus' Phillips Curve shift upward or did it shift downward?
A company has 4 plants: Plant 1, Plant 2, Plant 3, and Plant 4. All the plants make the same product The company sells the product in 4 different cities: City 1, City 2, City 3, City 4. Maximum production (in thousands of units) that is possible at the 4 plants are given respectively by (Plant 1 to Plant 4): 5, 25, 10, and 15. Your forecast shows that the demand for the product (in thousands of units) in each of the cities is given by (City 1 to City 4): 15, 7, 9, 10. Your firm does not want to have any backorders or lost demand. The production & transportation cost for getting a product from any given plant to any given city if given blow: Plant 1 Plant 2 Plant 3 Plant 4 Production and Transportation Cost per 1000 units (Thousand $) City 1 City 2 1070 1260 1825 780 800 City 3 1400 1685 1540 1070 2425 1355 843 City 4 1530 1100 500 1045 You need to decide which plant will serve which city and how much. Find the optimal way to serve the demands in all the cities. What is the optimal…
1. Write a linear program for the problem. 2. What is the optimal production mix among different coffee varieties and the profit associated with it? 3. What should be the per bag profit of Tarrazu which will make it beneficial to produce this variety? 4. One Cup is considering increasing the weekly bags to 150. If it costs One Cup $3.00 per bag to procure beans of any variety. Conduct sensitivity analysis and determine if One Cup should consider increasing the per week production. 5. Identify the range over which per bag profit of Sumatra and Kona may vary and still retain the current production plan as optimal for One Cup. 6. Once roasted the coffee beans must be preserved properly. To ensure that, One Cup Coffee is considering investing in a vacuum packaging machine for 24 hours/ week. It takes 10, 15 and 10 minutes to pack a bag of Sumatra, Kona and Tarazzu respectively. Identify if the current production plan will suit the installation of the new packaging scheme.

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