Consider the following linear program.Max 3A + 2Bs.t.1A1B ≤ 103A + 1B ≤ 221A + 2B ≤18A, B ≥ 0(a) Use the graphical solution procedure to find the optimal solution.What is the value of the objective function at the optimal solution?at (A, B) :=(b) Assume that the objective function coefficient for A changes from 3 to 5. Use the graphical solution procedure to find the new optimal solution.Does the optimal solution change?The extreme point---Select--- optimal. The value of the objective function becomes(c) Assume that the objective function coefficient for A remains 3, but the objective function coefficient for B changes from 2 to 4. Use the graphical solutionprocedure to find the new optimal solution.Does the optimal solution change?The extreme point---Select--- optimal. The value of the objective function becomes

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

Answered: (a) Use the graphical solution…

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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Mike Thatcher is a sales manager for an automobile dealership in Alberta. Mike earns a bonus each year based on revenue generated by the number of vehicles sold in the year less related warranty expenses. The quality of automobiles sold each year seems to vary since the warranty experience related to vehicles sold is highly variable. The actual warranty expenses have varied over the past 10 years from a low of 3% of an automobile’s selling price to a high of 10%. In the past, Mike has tended toward estimating warranty expenses on the high end just to be prudent. It is the end of the year and once again he must work with the dealership’s accountant in arriving at the warranty expense accrual for the cars sold this year. Required 1. Does the warranty accrual decision present any kind of ethical dilemma for Mike Thatcher? 2. Since the warranty experience is not constant, what percent do you think Mike should choose for this year? Justify your response.
Devise a solution for the problem under each of the four criteria of decisions under uncertainty.
d) The profit per unit for deluxe model was increased to 150 per unit. Evaluate the effect e) . Identify the range of optimality for each objective function coefficient (unit profit).Suppose the profit for the economy model is increased by $6 per unit, the profit for thestandard model is decreased by $2 per unit, and the profit for the deluxe model is increased by $4 per unit. ( use the 100% rule)What will be the new optimal solution be? f) If the number of fan motors available for production is increased by 100, evaluate theeffect.
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?
Sensitivity analysis in linear programming is used to: a) Determine the effect of changes in the coefficients of the objective function b) Determine the effect of changes in the right-hand side of constraints c) Both a and b d) Neither a nor b
For your next 10k race of the athletics season, you consider competing in either Sheffield, Cardiff, or Birmingham. After considering results from past years and the three different routes, you estimate your prize money, which will also depend on your form on the day. These estimated prizes are shown in the following table: Good form Average form Bad form 0 Sheffield 1000 Cardiff 700 Birmingham 800 400 500 600 200 100 Which condition must a satisfy such that Birmingham is the optimal city to go compete, according to the optimism-pessimism rule?
HITACHI LTD. an air conditioner manufacturer, produces 'x' sets per week at a total cost of x2+780x+25000. The firm is a monopolist and the demand function for its product is x = (15000 - ), where the price is 'p' per set. 4 (i) Determine the number of AC sets to be produced per week at which the firm will earn maximum net revenue; and (ii) Decide the monopoly price.
Osteoporosis is a degenerative disease that primarily affects women over the age of 60. A research analyst wants to forecast sales of StrongBones, a prescription drug for treating this debilitating disease. She uses the model Sales = B0 + B1 Population + B2 Income + E, where Sales is the sales of Strong Bones (in $1,000,000s), Population is the number of women over the age of 60 (in millions), and Income is the average income of women over the age of 60 (in $1,000s). She collects data on 32 cities across the United States and obtains the following regression results: Coefficients Standard Error t Stat p-Value Intercept Population Income 10.01 3.93 2.55 0.0231 8.19 2.20 3.72 0.0338 7.24 6.40 1.13 0.3758 a. What is the sample regression equation? Note: Enter your answers in millions rounded to 2 decimal places. Sales = Population + Income b-1. Interpret the coefficient of population. As the number of women over the age of 60 increases by 1 million, sales of Strong Bones is predicted to…
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?
2 Vidhya Balan is planning to liquidate her investments in mutual funds and invest in real estate. Before making the change to her investment strategy, Vidhya wants to forecast the price of mutual funds for the next 2 months. She has collected the following data on the average fund prices for the past 10 months. Average Month Fund Price 1. 55.1 53.8 3 53.4 4 52.95 5 52.15 6. 52.75 7 52.65 8 51.5 9. 52.25 10 51.7 Using a five-period moving average, forecast the a average fund price for Period 11. b. |Using exponential smoothing with a = 0.3 forecast the average fund price for Period 11. Assume an initial forecast for Month 2 (F2) as 55.10
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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